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Journal articles on the topic 'Reinsurance claims'

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Published: 4 June 2021

Last updated: 25 January 2023

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1

Saputra, Jumadil, Tika Fauzia, Sukono Sukono, and Riaman Riaman. "Estimation of Reinsurance Risk Value Using the Excess of Loss Method." International Journal of Business, Economics, and Social Development 1, no. 1 (June 12, 2020): 31–39. http://dx.doi.org/10.46336/ijbesd.v1i1.16.

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As with any other business that has a risk of any incident in the future, the insurance business also needs protection against the risks that may arise in the company so that the company does not lose. Therefore, the need for anticipation in organizing any claims submitted by the insurance company to Reinsurance Company so that insurance company may assign any or all of the risks to reinsurance companies. In the method of reinsurance excess-of-loss there is a certain retention limits that allow reinsurance companies bear no claims incurred on insurance companies. The results of this study showed the average occurrence of claims and the risks that may be encountered by Reinsurance Company during the period of insurance. The magnitude of the risk assumed by the reinsurer relies on the model claims aggregation formed from individual claim size distribution models and distribution models the number of claims incurred in the period of insurance. Besides the magnitude of risk was also determined from the retention limit of insurance and reinsurance method used.

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2

Ladoucette, Sophie A., and Jef L. Teugels. "Reinsurance of large claims." Journal of Computational and Applied Mathematics 186, no. 1 (February 2006): 163–90. http://dx.doi.org/10.1016/j.cam.2005.03.069.

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3

Kremer, Erhard. "Largest Claims Reinsurance Premiums under Possible Claims Dependence." ASTIN Bulletin 28, no. 2 (November 1998): 257–67. http://dx.doi.org/10.2143/ast.28.2.519069.

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4

Kremer, Erhard. "Largest claims reinsurance premiums under discrete claims sizes." Blätter der DGVFM 25, no. 3 (April 2002): 535–40. http://dx.doi.org/10.1007/bf02808465.

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5

Xiao, Yun, and Zhijian Qiu. "Research on Optimal Investment Reinsurance of Insurance Companies under Delayed Risk Model." Mathematical Problems in Engineering 2021 (December 27, 2021): 1–10. http://dx.doi.org/10.1155/2021/9287659.

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The reinsurance and investment portfolio of insurance companies has always been a hot issue in insurance business. In insurance practice, it is inevitable for insurance companies to invest their own funds in order to expand their capital scale and enhance market competitiveness so as to obtain greater returns. At the same time, in order for insurance companies to disperse insurance risks and to avoid too concentrated claims or catastrophes caused by failure to perform compensation responsibilities, the purchase of reinsurance business has also become an important way. Stochastic control theory is widely used in reinsurance and investment issues. Based on the reinsurance system architecture, this paper establishes a reinsurance delay risk investment model, which reduces the amount of claims to be borne by buying proportional reinsurance to avoid bankruptcy caused by the excessive amount of claims. By using the delayed venture capital model to describe the earnings of insurance companies, the optimal investment and reinsurance strategy are solved under the optimization criterion of minimizing the probability of bankruptcy. By analyzing the model parameter data, the influence of each parameter on optimal investment strategy and optimal reinsurance strategy is discussed.

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6

Kremer, Erhard. "Recursive largest claims reinsurance rating, revisited." Blätter der DGVFM 21, no. 4 (October 1994): 457–69. http://dx.doi.org/10.1007/bf02809486.

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7

Kremer, Erhard. "The Asymptotic Efficiency of Largest Claims Reinsurance Treaties." ASTIN Bulletin 20, no. 1 (April 1990): 11–22. http://dx.doi.org/10.2143/ast.20.1.2005480.

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AbstractReinsurance treaties defined as generalizations of the classical largest claims reinsurance covers are investigated with respect to the associated risk, defined as the variance of the insurer's retaining total claims amount. Instead of the unhandy variance corresponding handier asymptotic expressions are used. With these an asymptotic efficiency measure for comparing two such reinsurance covers is defined. It is shown that with respect to asymptotic efficiency the excess-of-loss treaty is better than the classical largest claims treaty. Furthermore the problem of giving optimal wheights to the ordered claims of a generalized largest claims cover is discussed.

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8

Kremer, E. "The total claims amount of largest claims reinsurance treaties revisited." Insurance: Mathematics and Economics 13, no. 2 (November 1993): 163. http://dx.doi.org/10.1016/0167-6687(93)90914-b.

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9

Kremer, Erhard. "The total claims amount of largest claims reinsurance treaties revisited." Blätter der DGVFM 20, no. 4 (October 1992): 431–39. http://dx.doi.org/10.1007/bf02808435.

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10

Berglund, Raoul M. "A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover." ASTIN Bulletin 28, no. 1 (May 1998): 153–62. http://dx.doi.org/10.2143/ast.28.1.519084.

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AbstractIn the present paper the author gives net premium formulae for a generalized largest claims reinsurance cover. If the claim sizes are mutually independent and identically 3-parametric Pareto distributed and the number of claims has a Poisson, binomial or negative binomial distribution, formulae are given from which numerical values can easily be obtained. The results are based on identities for compounded order statistics.

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11

Li, Sheng, and Yong He. "Optimal Time-Consistent Investment and Reinsurance Strategy Under Time Delay and Risk Dependent Model." Mathematical Problems in Engineering 2020 (August 28, 2020): 1–20. http://dx.doi.org/10.1155/2020/9368346.

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In this paper, we consider the problem of investment and reinsurance with time delay under the compound Poisson model of two-dimensional dependent claims. Suppose an insurance company controls the claim risk of two kinds of dependent insurance businesses by purchasing proportional reinsurance and invests its wealth in a financial market composed of a risk-free asset and a risk asset. The risk asset price process obeys the geometric Brownian motion. By introducing the capital flow related to the historical performance of the insurer, the wealth process described by stochastic delay differential equation (SDDE) is obtained. The extended HJB equation is obtained by using the stochastic control theory under the framework of game theory. Under the reinsurance expected premium principle, optimal time-consistent investment and reinsurance strategy and the corresponding value function are obtained. Finally, the influence of model parameters on the optimal strategy is explained by numerical analysis.

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12

Badescu, Andrei L., Eric C. K. Cheung, and Landy Rabehasaina. "A Two-Dimensional Risk Model with Proportional Reinsurance." Journal of Applied Probability 48, no. 3 (September 2011): 749–65. http://dx.doi.org/10.1239/jap/1316796912.

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In this paper we consider an extension of the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008a). To this end, we assume that there are two insurers. The first insurer is subject to claims arising from two independent compound Poisson processes. The second insurer, which can be viewed as a different line of business of the same insurer or as a reinsurer, covers a proportion of the claims arising from one of these two compound Poisson processes. We derive the Laplace transform of the time until ruin of at least one insurer when the claim sizes follow a general distribution. The surplus level of the first insurer when the second insurer is ruined first is discussed at the end in connection with some open problems.

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13

Badescu, Andrei L., Eric C. K. Cheung, and Landy Rabehasaina. "A Two-Dimensional Risk Model with Proportional Reinsurance." Journal of Applied Probability 48, no. 03 (September 2011): 749–65. http://dx.doi.org/10.1017/s0021900200008299.

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In this paper we consider an extension of the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008a). To this end, we assume that there are two insurers. The first insurer is subject to claims arising from two independent compound Poisson processes. The second insurer, which can be viewed as a different line of business of the same insurer or as a reinsurer, covers a proportion of the claims arising from one of these two compound Poisson processes. We derive the Laplace transform of the time until ruin of at least one insurer when the claim sizes follow a general distribution. The surplus level of the first insurer when the second insurer is ruined first is discussed at the end in connection with some open problems.

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14

Frees, Edward W., Peng Shi, and Emiliano A. Valdez. "Actuarial Applications of a Hierarchical Insurance Claims Model." ASTIN Bulletin 39, no. 1 (May 2009): 165–97. http://dx.doi.org/10.2143/ast.39.1.2038061.

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AbstractThis paper demonstrates actuarial applications of modern statistical methods that are applied to detailed, micro-level automobile insurance records. We consider 1993-2001 data consisting of policy and claims files from a major Singaporean insurance company. A hierarchical statistical model, developed in prior work (Frees and Valdez (2008)), is fit using the micro-level data. This model allows us to study the accident frequency, loss type and severity jointly and to incorporate individual characteristics such as age, gender and driving history that explain heterogeneity among policyholders.Based on this hierarchical model, one can analyze the risk profile of either a single policy (micro-level) or a portfolio of business (macro-level). This paper investigates three types of actuarial applications. First, we demonstrate the calculation of the predictive mean of losses for individual risk rating. This allows the actuary to differentiate prices based on policyholder characteristics. The nonlinear effects of coverage modifications such as deductibles, policy limits and coinsurance are quantified. Moreover, our flexible structure allows us to “unbundle” contracts and price more primitive elements of the contract, such as coverage type. The second application concerns the predictive distribution of a portfolio of business. We demonstrate the calculation of various risk measures, including value at risk and conditional tail expectation, that are useful in determining economic capital for insurance companies. Third, we examine the effects of several reinsurance treaties. Specifically, we show the predictive loss distributions for both the insurer and reinsurer under quota share and excess-of-loss reinsurance agreements. In addition, we present an example of portfolio reinsurance, in which the combined effect of reinsurance agreements on the risk characteristics of ceding and reinsuring company are described.

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15

Albrecher, Hansjörg, Bohan Chen, Eleni Vatamidou, and Bert Zwart. "Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes." Journal of Applied Probability 57, no. 2 (June 2020): 513–30. http://dx.doi.org/10.1017/jpr.2020.8.

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AbstractWe investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result by leveraging recent developments on sample-path large deviations for heavy tails. Our results allow, on the asymptotic level, for an explicit comparison between two well-known large-claim reinsurance contracts, namely LCR and ECOMOR. Finally, we assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.

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16

Kremer, E. "Fourier methods for the claims amounts of largest claims reinsurance covers." Insurance: Mathematics and Economics 13, no. 2 (November 1993): 162. http://dx.doi.org/10.1016/0167-6687(93)90910-h.

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17

Kremer, Erhard. "Fourier methods for the claims amounts of largest claims reinsurance covers." Blätter der DGVFM 20, no. 1 (April 1991): 31–35. http://dx.doi.org/10.1007/bf02818379.

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18

Kremer, Erhard. "A General Bound for the Net Premium of the Largest Claims Reinsurance Covers." ASTIN Bulletin 18, no. 1 (April 1988): 69–78. http://dx.doi.org/10.2143/ast.18.1.2014961.

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AbstractFor a general class of reinsurance treaties the author gives an upper bound for the net premium. This result can be seen as the counterpart to a premium bound for the classical stop-loss reinsurance cover (see Bowers, 1969). For some special cases some preliminary work can be found in Kremer (1983).

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19

Hürlimann, Werner. "Excess of Loss Reinsurance with Reinstatements Revisited." ASTIN Bulletin 35, no. 01 (May 2005): 211–38. http://dx.doi.org/10.2143/ast.35.1.583173.

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The classical evaluation of pure premiums for excess of loss reinsurance with reinstatements requires the knowldege of the claim size distribution of the insurance risk. In the situation of incomplete information, where only a few characteristics of the aggregate claims to an excess of loss layer can be estimated, the method of stop-loss ordered bounds yields a simple analytical distribution-free approximation to pure premiums of excess of loss reinsurance with reinstatements. It is shown that the obtained approximation is enough accurate for practical purposes and improves the analytical approximations obtained using either a gamma, translated gamma, translated inverse Gaussian or a mixture of the last two distributions.

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20

Hürlimann, Werner. "Excess of Loss Reinsurance with Reinstatements Revisited." ASTIN Bulletin 35, no. 1 (May 2005): 211–38. http://dx.doi.org/10.1017/s0515036100014136.

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The classical evaluation of pure premiums for excess of loss reinsurance with reinstatements requires the knowldege of the claim size distribution of the insurance risk. In the situation of incomplete information, where only a few characteristics of the aggregate claims to an excess of loss layer can be estimated, the method of stop-loss ordered bounds yields a simple analytical distribution-free approximation to pure premiums of excess of loss reinsurance with reinstatements. It is shown that the obtained approximation is enough accurate for practical purposes and improves the analytical approximations obtained using either a gamma, translated gamma, translated inverse Gaussian or a mixture of the last two distributions.

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21

Hipp, Christian, and Michael Vogt. "Optimal Dynamic XL Reinsurance." ASTIN Bulletin 33, no. 02 (November 2003): 193–207. http://dx.doi.org/10.2143/ast.33.2.503690.

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We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.

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22

Hipp, Christian, and Michael Vogt. "Optimal Dynamic XL Reinsurance." ASTIN Bulletin 33, no. 2 (November 2003): 193–207. http://dx.doi.org/10.1017/s051503610001343x.

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We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.

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23

Han, Chang-Wan. "A Study on Claims Clauses in Reinsurance Contract." Korea Financial Law Association 12, no. 1 (April 30, 2015): 193–222. http://dx.doi.org/10.15692/kjfl.12.1.7.

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24

Korn, Ralf, Olaf Menkens, and Mogens Steffensen. "Worst-case-optimal dynamic reinsurance for large claims." European Actuarial Journal 2, no. 1 (July 2012): 21–48. http://dx.doi.org/10.1007/s13385-012-0050-8.

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25

Hashorva, Enkelejd, and Jinzhu Li. "ECOMOR and LCR reinsurance with gamma-like claims." Insurance: Mathematics and Economics 53, no. 1 (July 2013): 206–15. http://dx.doi.org/10.1016/j.insmatheco.2013.05.004.

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26

Kremer, E. "The asymptotic efficiency of largest claims reinsurance treaties." Insurance: Mathematics and Economics 12, no. 1 (February 1993): 72. http://dx.doi.org/10.1016/0167-6687(93)91025-p.

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27

Kremer, Erhard. "Largest claims reinsurance premiums for the Weibull model." Blätter der DGVFM 23, no. 3 (April 1998): 279–83. http://dx.doi.org/10.1007/bf02808290.

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28

Dickson, David C. M., and Howard R. Waters. "Optimal Dynamic Reinsurance." ASTIN Bulletin 36, no. 02 (November 2006): 415–32. http://dx.doi.org/10.2143/ast.36.2.2017928.

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We consider a classical surplus process where the insurer can choose a different level of reinsurance at the start of each year. We assume the insurer’s objective is to minimise the probability of ruin up to some given time horizon, either in discrete or continuous time. We develop formulae for ruin probabilities under the optimal reinsurance strategy, i.e. the optimal retention each year as the surplus changes and the period until the time horizon shortens. For our compound Poisson process, it is not feasible to evaluate these formulae, and hence determine the optimal strategies, in any but the simplest cases. We show how we can determine the optimal strategies by approximating the (compound Poisson) aggregate claims distributions by translated gamma distributions, and, alternatively, by approximating the compound Poisson process by a translated gamma process.

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29

Dickson, David C. M., and Howard R. Waters. "Optimal Dynamic Reinsurance." ASTIN Bulletin 36, no. 2 (November 2006): 415–32. http://dx.doi.org/10.1017/s0515036100014574.

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We consider a classical surplus process where the insurer can choose a different level of reinsurance at the start of each year. We assume the insurer’s objective is to minimise the probability of ruin up to some given time horizon, either in discrete or continuous time. We develop formulae for ruin probabilities under the optimal reinsurance strategy, i.e. the optimal retention each year as the surplus changes and the period until the time horizon shortens. For our compound Poisson process, it is not feasible to evaluate these formulae, and hence determine the optimal strategies, in any but the simplest cases. We show how we can determine the optimal strategies by approximating the (compound Poisson) aggregate claims distributions by translated gamma distributions, and, alternatively, by approximating the compound Poisson process by a translated gamma process.

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30

Meng, Hui, Ming Zhou, and Tak Kuen Siu. "OPTIMAL DIVIDEND–REINSURANCE WITH TWO TYPES OF PREMIUM PRINCIPLES." Probability in the Engineering and Informational Sciences 30, no. 2 (December 9, 2015): 224–43. http://dx.doi.org/10.1017/s0269964815000352.

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A combined optimal dividend/reinsurance problem with two types of insurance claims, namely the expected premium principle and the variance premium principle, is discussed. Dividend payments are considered with both fixed and proportional transaction costs. The objective of an insurer is to determine an optimal dividend–reinsurance policy so as to maximize the expected total value of discounted dividend payments to shareholders up to ruin time. The problem is formulated as an optimal regular-impulse control problem. Closed-form solutions for the value function and optimal dividend–reinsurance strategy are obtained in some particular cases. Finally, some numerical analysis is given to illustrate the effects of safety loading on optimal reinsurance strategy.

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31

LIN, XIANG, and PENG YANG. "OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL." ANZIAM Journal 52, no. 3 (January 2011): 250–62. http://dx.doi.org/10.1017/s144618111100068x.

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AbstractWe consider an insurance company whose surplus is governed by a jump diffusion risk process. The insurance company can purchase proportional reinsurance for claims and invest its surplus in a risk-free asset and a risky asset whose return follows a jump diffusion process. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equation, closed-form solutions for the value function as well as the optimal investment and proportional reinsurance policy are obtained. We also discuss the effects of parameters on the optimal investment and proportional reinsurance policy by numerical calculations.

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32

Craighead, D. H. "Reserving for catastrophe reinsurance." Journal of the Institute of Actuaries 121, no. 1 (1994): 135–60. http://dx.doi.org/10.1017/s0020268100020114.

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AbstractThe paper sets out the method required to be followed when estimating reserves for a Company or a Lloyd's Syndicate which has accepted reinsurance treaties that have given rise to catastrophe losses, sufficiently large to upset the normal development pattern and to affect the gross account quite differently from the net account. The losses may be caused by single factors such as aircraft crashes or oil rig disasters, or by the aggregation of claims resulting from a windstorm or an earthquake. The paper discusses two possible approaches to estimation of the gross losses; via exposure totals or via statistical modelling techniques.

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33

Hesselager, Ole. "A Class of Conjugate Priors with Applications to Excess-of-Loss Reinsurance." ASTIN Bulletin 23, no. 1 (May 1993): 77–93. http://dx.doi.org/10.2143/ast.23.1.2005102.

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AbstractWe consider the problem of forecasting the total cost of claims in excess-of-loss reinsurance. The number of claims reported to the direct insurer is assumed to follow a Poisson law, and the claim severities are modelled by a Pareto distribution. The Poisson frequency as well as the Pareto parameter will be considered as random parameters in a Bayesian setting. We derive the class of conjugate joint prior distributions, which turn out to specify a (prior) dependence between the two parameters. The use of conjugate priors facilitates the mathematical analysis, and it also makes it easy to interpret the parameters of the prior distribution.

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34

QIAN, YIPING, and XIANG LIN. "RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS." ANZIAM Journal 51, no. 1 (July 2009): 34–48. http://dx.doi.org/10.1017/s144618110900042x.

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AbstractIn this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations.

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35

Eisenberg, Julia, and Hanspeter Schmidli. "Optimal Control of Capital Injections by Reinsurance with a Constant Rate of Interest." Journal of Applied Probability 48, no. 3 (September 2011): 733–48. http://dx.doi.org/10.1239/jap/1316796911.

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We consider a classical risk model and its diffusion approximation, where the individual claims are reinsured by a reinsurance treaty with deductible b ∈ [0, b̃]. Here b = b̃ means ‘no reinsurance’ and b= 0 means ‘full reinsurance’. In addition, the insurer is allowed to invest in a riskless asset with some constant interest rate m > 0. The cedent can choose an adapted reinsurance strategy {bt}t≥0, i.e. the parameter can be changed continuously. If the surplus process becomes negative, the cedent has to inject additional capital. Our aim is to minimise the expected discounted capital injections over all admissible reinsurance strategies. We find an explicit expression for the value function and the optimal strategy using the Hamilton-Jacobi-Bellman approach in the case of a diffusion approximation. In the case of the classical risk model, we show the existence of a ‘weak’ solution and calculate the value function numerically.

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36

Hess, Klaus Th, Anett Liewald, and Klaus D. Schmidt. "An Extension of Panjer's Recursion." ASTIN Bulletin 32, no. 2 (November 2002): 283–97. http://dx.doi.org/10.2143/ast.32.2.1030.

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AbstractSundt and Jewell have shown that a nondegenerate claim number distribution Q = {qn}nϵN0 satisfies the recursionfor all n≥0 if and only if Q is a binomial, Poisson or negativebinomial distribution. This recursion is of interest since it yields a recursion for the aggregate claims distribution in the collective model of risk theory when the claim size distribution is integer-valued as well. A similar characterization of claim number distributions satisfying the above recursion for all n ≥ 1 has been obtained by Willmot. In the present paper we extend these results and the subsequent recursion for the aggregate claims distribution to the case where the recursion holds for all n ≥ k with arbitrary k. Our results are of interest in catastrophe excess-of-loss reinsurance.

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37

Eisenberg, Julia, and Hanspeter Schmidli. "Optimal Control of Capital Injections by Reinsurance with a Constant Rate of Interest." Journal of Applied Probability 48, no. 03 (September 2011): 733–48. http://dx.doi.org/10.1017/s0021900200008287.

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We consider a classical risk model and its diffusion approximation, where the individual claims are reinsured by a reinsurance treaty with deductible b ∈ [0, b̃]. Here b = b̃ means ‘no reinsurance’ and b= 0 means ‘full reinsurance’. In addition, the insurer is allowed to invest in a riskless asset with some constant interest rate m > 0. The cedent can choose an adapted reinsurance strategy {b t } t≥0, i.e. the parameter can be changed continuously. If the surplus process becomes negative, the cedent has to inject additional capital. Our aim is to minimise the expected discounted capital injections over all admissible reinsurance strategies. We find an explicit expression for the value function and the optimal strategy using the Hamilton-Jacobi-Bellman approach in the case of a diffusion approximation. In the case of the classical risk model, we show the existence of a ‘weak’ solution and calculate the value function numerically.

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38

Adhitama, Randitya Eko. "METODE REASURANSI QUOTA SHARE TREATY DITINJAU DARI HUKUM PERJANJIAN." Jurnal Hukum & Pembangunan 39, no. 2 (June 3, 2009): 173. http://dx.doi.org/10.21143/jhp.vol39.no2.208.

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AbstrakThis essay discusses the methods of quota share reinsurance treaty review ofthe applicable treaty law in indonesia. Writing this essay aims to find outlegal protection for client (Insured) when an insurance company (insurer) ismaking a reinsurance agreement with the company by using the methods ofquota share treaty, subject to sanctions such as Feezing efforts by theregulator and the responsibility for the insurance company (insurer) inviolation of the clause "claim cooperation clause" which are listed in thereinsurance agreement with the method of quota share treaty in handlingclaims. This research is using the literature research and field research.Results of this study suggest that the government create more regulations tohandling claims and required a special institution that can protect the rightsof customers in the consumer services in the areas of insurance

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39

Coutts, S. M., and T. R. H. Thomas. "Modelling the Impact of Reinsurance on Financial Strength." British Actuarial Journal 3, no. 3 (August 1, 1997): 583–653. http://dx.doi.org/10.1017/s1357321700005067.

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ABSTRACTThis paper develops the Daykin et al (1994) asset/liability model to examine specifically the effects of different reinsurance programmes on the capital of a direct insurance company. By modelling the gross premiums and claims separately from the impact of reinsurance on them, it is possible to examine directly the effects of different reinsurance programmes on a company's expected performance just as easily as changes in asset mix or business volumes. The paper goes on to discuss the necessary assumptions to be built into such a model, and then gives a worked example. The emphasis of the paper is on management reporting rather than on mathematical detail.

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40

Asimit, Alexandru V., and Bruce L. Jones. "Dependence and the asymptotic behavior of large claims reinsurance." Insurance: Mathematics and Economics 43, no. 3 (December 2008): 407–11. http://dx.doi.org/10.1016/j.insmatheco.2008.08.007.

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41

Kremer, Erhard. "Largest claims reinsurance premiums for the generalized Weibull model." Blätter der DGVFM 23, no. 3 (April 1998): 441–43. http://dx.doi.org/10.1007/bf02808306.

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42

Vilar-Zanón, José L., and Cristina Lozano-Colomer. "On Pareto Conjugate Priors and Their Application to Large Claims Reinsurance Premium Calculation." ASTIN Bulletin 37, no. 02 (November 2007): 405–28. http://dx.doi.org/10.2143/ast.37.2.2024074.

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This paper addresses the Bayesian estimation of the shape parameter of Pareto distributions, and its application to premium calculation of large claims excess of loss (XL) reinsurance contracts. It studies the use of the generalized inverse Gaussian (GIG) as a Pareto prior conjugate, a family that contains as a particular case the gamma distribution. An exact credibility formula is deduced allowing the calculation of individual reinsurance premiums. These are premiums suited to the excesses history of a sole portfolio. A family of predictive distributions for the excesses is derived. We apply our exact credibility model to a sample of excesses arisen in ten Spanish portfolios of liability motor insurance from year 1992 to year 2001.

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43

Vilar-Zanón, José L., and Cristina Lozano-Colomer. "On Pareto Conjugate Priors and Their Application to Large Claims Reinsurance Premium Calculation." ASTIN Bulletin 37, no. 2 (November 2007): 405–28. http://dx.doi.org/10.1017/s0515036100014938.

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Abstract:

This paper addresses the Bayesian estimation of the shape parameter of Pareto distributions, and its application to premium calculation of large claims excess of loss (XL) reinsurance contracts. It studies the use of the generalized inverse Gaussian (GIG) as a Pareto prior conjugate, a family that contains as a particular case the gamma distribution. An exact credibility formula is deduced allowing the calculation of individual reinsurance premiums. These are premiums suited to the excesses history of a sole portfolio. A family of predictive distributions for the excesses is derived. We apply our exact credibility model to a sample of excesses arisen in ten Spanish portfolios of liability motor insurance from year 1992 to year 2001.

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44

Dassios, Angelos, and Ji-Wook Jang. "Kalman-Bucy Filtering for Linear Systems Driven by the Cox Process with Shot Noise Intensity and Its Application to the Pricing of Reinsurance Contracts." Journal of Applied Probability 42, no. 1 (March 2005): 93–107. http://dx.doi.org/10.1239/jap/1110381373.

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In practical situations, we observe the number of claims to an insurance portfolio but not the claim intensity. It is therefore of interest to try to solve the ‘filtering problem’; that is, to obtain the best estimate of the claim intensity on the basis of reported claims. In order to use the Kalman-Bucy filter, based on the Cox process incorporating a shot noise process as claim intensity, we need to approximate it by a Gaussian process. We demonstrate that, if the primary-event arrival rate of the shot noise process is reasonably large, we can then approximate the intensity, claim arrival, and aggregate loss processes by a three-dimensional Gaussian process. We establish weak-convergence results. We then use the Kalman-Bucy filter and we obtain the price of reinsurance contracts involving high-frequency events.

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45

Dassios, Angelos, and Ji-Wook Jang. "Kalman-Bucy Filtering for Linear Systems Driven by the Cox Process with Shot Noise Intensity and Its Application to the Pricing of Reinsurance Contracts." Journal of Applied Probability 42, no. 01 (March 2005): 93–107. http://dx.doi.org/10.1017/s0021900200000085.

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Abstract:

In practical situations, we observe the number of claims to an insurance portfolio but not the claim intensity. It is therefore of interest to try to solve the ‘filtering problem’; that is, to obtain the best estimate of the claim intensity on the basis of reported claims. In order to use the Kalman-Bucy filter, based on the Cox process incorporating a shot noise process as claim intensity, we need to approximate it by a Gaussian process. We demonstrate that, if the primary-event arrival rate of the shot noise process is reasonably large, we can then approximate the intensity, claim arrival, and aggregate loss processes by a three-dimensional Gaussian process. We establish weak-convergence results. We then use the Kalman-Bucy filter and we obtain the price of reinsurance contracts involving high-frequency events.

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46

Noviyanti, Lienda, Achmad Zanbar Soleh, Anna Chadidjah, and Hasna Afifah Rusyda. "Optimal Retention for a Quota-Share Reinsurance." Jurnal Teknik Industri 20, no. 1 (June 17, 2018): 25–32. http://dx.doi.org/10.9744/jti.20.1.25-32.

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The Indonesian Financial Services Authority (OJK) has instructed all insurance providers in Indonesia to apply a mandatory tariff for property insurance. The tariff has to be uniformly applied and the rule of set the maximum and minimum premium rates for protection against losses. Furthermore, the OJK issued the new rule regarding self-retention and domestic reinsurance. Insurance companies are obliged to have and implement self-retention for each risk in accordance with the self-retention limits. Fluctuations of total premium income and claims may lead the insurance company cannot fulfil the obligation to the insured, thus the company needs to conduct reinsurance. Reinsurance helps protect insurers against unforeseen or extraordinary losses by allowing them to spread their risks. Because reinsurer chargers premium to the insurance company, a properly calculated optimal retention would be nearly as high as the insurer financial ability. This paper is aimed at determining optimal retentions indicated by the risk measure Value at Risk (VaR), Expected Shortfall (ES) and Minimum Variance (MV). Here we use the expectation premium principle which minimizes individual risks based on their quota share reinsurance. Regarding to the data in an insurance property, we use a bivariate lognormal distribution to obtain VaR, ES and MV, and a bivariate exponential distribution to obtain MV. The bivariate distributions are required to derive the conditional probability of the amount of claim occurs given the benefit has occurred.

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47

Asimit, Alexandru V., and Bruce L. Jones. "Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks." ASTIN Bulletin 38, no. 01 (May 2008): 147–59. http://dx.doi.org/10.2143/ast.38.1.2030407.

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We consider a dependent portfolio of insurance contracts. Asymptotic tail probabilities of the ECOMOR and LCR reinsurance amounts are obtained under certain assumptions about the dependence structure.

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Asimit, Alexandru V., and Bruce L. Jones. "Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks." ASTIN Bulletin 38, no. 1 (May 2008): 147–59. http://dx.doi.org/10.1017/s0515036100015105.

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We consider a dependent portfolio of insurance contracts. Asymptotic tail probabilities of the ECOMOR and LCR reinsurance amounts are obtained under certain assumptions about the dependence structure.

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49

Brachetta, Matteo, and Claudia Ceci. "Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models." Risks 7, no. 2 (May 1, 2019): 48. http://dx.doi.org/10.3390/risks7020048.

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We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer’s surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate r. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed.

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Kremer, E. "Recursive Calculation of the Net Premium for Largest Claims Reinsurance Covers." ASTIN Bulletin 16, no. 2 (November 1986): 101–8. http://dx.doi.org/10.2143/ast.16.2.2015002.

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AbstractIn the present paper the author investigates the problem of calculating the net premium for some versions of the largest claims reinsurance cover. A very handy recursive rating method is derived by applying some recursion formulas for the expectations of order statistics.

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