Academic literature on the topic 'Surplus treaty reinsurance'

AbstractThe primary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset. Under the above Black-Scholes type framework and using the objective of minimizing the ruin probability of the insurer, we formally establish that the excess-of-loss reinsurance treaty is optimal among the class of plausible reinsurance treaties. We also obtain the optimal level of retention as well as provide an explicit expression of the minimal probability of ruin.

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.

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.

In this paper, we study the optimal retentions for an insurer with a compound fractional Poisson surplus and a layer reinsurance treaty. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are obtained. It is demonstrated that the optimal retention vector and the maximal adjustment coefficient are not only closely related to the parameter of the fractional Poisson process, but also dependent on the time and the claim intensity, which is different from the case in the classical compound Poisson process. Numerical examples are presented to show the impacts of the three parameters on the optimal results.

Mestrado em Ciências Actuariais
Um dos objetivos do regime Solvência II é melhorar a qualidade de gestão do risco, aumentar a flexibilidade para as seguradoras e resseguradoras gerirem os seus ativos e passivos de acordo com o seu perfil de risco e, ainda, reforçar a protecção dos segurados. Nesta matéria, o resseguro permite a transferência de riscos e, consequentemente, economias ao nível dos requisitos de capital. O objetivo deste trabalho é compreender como o resseguro afeta os requisitos de capital em contexto Solvência I e Solvência II, neste último caso quando as empresas de seguros e resseguros utilizam uma abordagem baseada num modelo interno.
One of the aims of Solvency II regime is improve the risk management quality, increase flexibility for insurers and reinsurers to manage their assets and liabilities according to their risk profile and further enhance the protection of policyholders. In addition, the use of reinsurance allows the transfer of risks and therefore savings in terms of capital requirements. The aim of this work is to understand how the reinsurance affects the capital requirements in context Solvency I and Solvency II, in the latter case when insurance and reinsurance companies use an approach based on an internal model.
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