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Journal articles on the topic 'CRRA utility function'

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Published: 4 June 2021

Last updated: 2 February 2022

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Fleissig, Adrian R., A. Ronald Gallant, and John J. Seater. "SEPARABILITY, AGGREGATION, AND EULER EQUATION ESTIMATION." Macroeconomic Dynamics 4, no. 4 (2000): 547–72. http://dx.doi.org/10.1017/s1365100500017077.

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We derive a seminonparametric utility function containing the constant relative risk aversion (CRRA) function as a special case, and we estimate the associated Euler equations with U.S. consumption data. There is strong evidence that the CRRA function is misspecified. The correctly specified function includes lagged effects of durable goods and perhaps nondurable goods, is bounded as required by Arrow's Utility Boundedness Theorem, and has a positive rate of time preference. Constraining sample periods and separability structure to be consistent with the generalized axiom of revealed preference affects estimation results substantially. Using Divisia aggregates instead of the NIPA aggregates also affects results.

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Georgescu, Irina, and Jani Kinnunen. "Optimal Saving by Expected Utility Operators." Axioms 9, no. 1 (2020): 17. http://dx.doi.org/10.3390/axioms9010017.

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This paper studies an optimal saving model in which risk is represented by a fuzzy number and the total utility function of the model is defined by an expected utility operator. This model generalizes some existing possibilistic saving models and from them, by a particularization, one can obtain new saving models. In the paper, sufficient conditions are set for the presence of potential risk to increase optimal saving levels and an approximation formula for optimal saving is demonstrated. Particular models for a few concrete expected utility operators are analyzed for triangular fuzzy numbers and CRRA-utility functions.

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Gong, Mingming, and Shulin Liu. "A First-Price Sealed-Bid Asymmetric Auction When Two Bidders Have Respective CRRA and General Utility Functions." Discrete Dynamics in Nature and Society 2021 (September 3, 2021): 1–15. http://dx.doi.org/10.1155/2021/5592402.

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We study a first-price auction with two bidders where one bidder is characterized by a constant relative risk aversion utility function (i.e., a concave power function) while the other has a general concave utility function. We establish the existence and uniqueness of the optimal strategic markups and analyze the effects of one bidder’s risk aversion level on the optimal strategic markups of him and his opponent’s, the allocative efficiency of the auction, and the seller’s expected revenue, respectively.

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Deelstra, Griselda, Martino Grasselli, and Pierre-François Koehl. "Optimal investment strategies in a CIR framework." Journal of Applied Probability 37, no. 04 (2000): 936–46. http://dx.doi.org/10.1017/s0021900200018131.

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We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

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Deelstra, Griselda, Martino Grasselli, and Pierre-François Koehl. "Optimal investment strategies in a CIR framework." Journal of Applied Probability 37, no. 4 (2000): 936–46. http://dx.doi.org/10.1239/jap/1014843074.

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Akdeniz, Levent, and W. Davis Dechert. "THE EQUITY PREMIUM IN CONSUMPTION AND PRODUCTION MODELS." Macroeconomic Dynamics 16, S1 (2012): 139–48. http://dx.doi.org/10.1017/s1365100511000708.

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In this paper we use a simple model with a single Cobb–Douglas firm and a consumer with a CRRA utility function to show the difference between the equity premia in the production-based Brock model and the consumption-based Lucas model. With this simple example we show that the equity premium in the production-based model exceeds that of the consumption-based model with probability 1.

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KINGSTON, GEOFFREY, and SUSAN THORP. "Annuitization and asset allocation with HARA utility." Journal of Pension Economics and Finance 4, no. 3 (2005): 225–48. http://dx.doi.org/10.1017/s1474747205002088.

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A new explanation for the well-known reluctance of retirees to buy life annuities is due to Milevsky and Young (2002, 2003): Since the decision to purchase longevity insurance is largely irreversible, in uncertain environments a real option to delay annuitization (RODA) generally has value. Milevsky and Young analytically identify and numerically estimate the RODA in a setting of constant relative risk aversion. This paper presents an extension to the case of HARA (or GLUM) preferences, the simplest representation of a consumption habit. The precise date of annuitization can no longer be ascertained with certainty in advance. This paper derives an approximation whereby the agent precommits. The effect of increasing the subsistence consumption rate on the timing of annuity purchase is similar to the effect of increasing the curvature parameter of the utility function. As in the CRRA case studied by Milevsky and Young, delayed annuitization is associated with optimistic predictions of the Sharpe ratio and divergence between annuity purchaser and provider predictions of mortality.

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Wen, Yuzhen, and Chuancun Yin. "Optimal Expected Utility of Dividend Payments with Proportional Reinsurance under VaR Constraints and Stochastic Interest Rate." Journal of Function Spaces 2020 (August 11, 2020): 1–13. http://dx.doi.org/10.1155/2020/4051969.

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In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.

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Fernandes, Ana. "A CLOSED-FORM SOLUTION TO A MODEL OF TWO-SIDED, PARTIAL ALTRUISM." Macroeconomic Dynamics 16, no. 2 (2012): 230–39. http://dx.doi.org/10.1017/s1365100510000064.

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This paper presents a closed-form characterization of the allocation of resources in an overlapping generations model of two-sided, partial altruism. Three assumptions are made: (i) parents and children play Markov strategies, (ii) utility takes the CRRA form, and (iii) the income of children is stochastic but proportional to the saving of parents. In families where children are rich relative to their parents, saving rates—measured as a function of the family's total resources—are higher than when children are poor relative to their parents. Income redistribution from the old to the young, therefore, leads to an increase in aggregate saving.

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Shiraishi, Hiroshi. "A Simulation Approach to Statistical Estimation of Multiperiod Optimal Portfolios." Advances in Decision Sciences 2012 (June 5, 2012): 1–13. http://dx.doi.org/10.1155/2012/341476.

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This paper discusses a simulation-based method for solving discrete-time multiperiod portfolio choice problems under AR(1) process. The method is applicable even if the distributions of return processes are unknown. We first generate simulation sample paths of the random returns by using AR bootstrap. Then, for each sample path and each investment time, we obtain an optimal portfolio estimator, which optimizes a constant relative risk aversion (CRRA) utility function. When an investor considers an optimal investment strategy with portfolio rebalancing, it is convenient to introduce a value function. The most important difference between single-period portfolio choice problems and multiperiod ones is that the value function is time dependent. Our method takes care of the time dependency by using bootstrapped sample paths. Numerical studies are provided to examine the validity of our method. The result shows the necessity to take care of the time dependency of the value function.

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Soriano-Morales, Yazmín Viridiana, Benjamín Vallejo-Jiménez, and Francisco Venegas-Martínez. "Impact of the degree of relative risk aversion, the interest rate and the exchange rate depreciation on economic welfare in a small open economy." PANORAMA ECONÓMICO 13, no. 25 (2018): 18. http://dx.doi.org/10.29201/pe-ipn.v13i25.175.

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This paper is aimed at assessing the impact of the degree of relative risk aversion on economic welfare for different levels of the interest rate and the exchange rate depreciation in a small open beconomy. To do this, a representative consumer-producer makes decisions on consumption, money balances, and leisure. In order to find a closed-form solution of the household’s economic welfare, it is assumed that individual’s preferences belong to the family of Constant Relative Risk Aversion (CRRA) utility functions. Several comparative statics graphical experiments about the effects of the degree of relative risk aversion on economic welfare for different levels of nominal variables are carried out. Finally, we find that, under the stated assumptions, household’s economic welfare seen as a function of the degree of relative risk aversion is responsive to different values of nominal variables.

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Chiu, Mei Choi, and Hoi Ying Wong. "Optimal Investment for Insurers with the Extended CIR Interest Rate Model." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/129474.

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A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

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Hu, Chunhua, Wenyi Huang, and Tianhao Xie. "The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains." Mathematical Problems in Engineering 2020 (February 11, 2020): 1–21. http://dx.doi.org/10.1155/2020/4353025.

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A wealth distribution model on isolated discrete time domains, which allows the wealth to exchange at irregular time intervals, is used to describe the effect of agent’s trading behavior on wealth distribution. We assume that the agents have different degrees of risk aversion. The hyperbolic absolute risk aversion (HARA) utility function is employed to describe the degrees of risk aversion of agents, including decreasing relative risk aversion (DRRA), increasing relative risk aversion (IRRA), and constant relative risk aversion (CRRA). The effect of agent’s expectation on wealth distribution is taken into account in our wealth distribution model, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth status. The Euler equation and transversality condition for the model on isolated discrete time domains are given to prove the existence of the optimal solution of the model. The optimal solution of the wealth distribution model is obtained by using the method of solving the rational expectation model on isolated discrete time domains. A numerical example is given to highlight the advantages of the wealth distribution model.

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Gomes, Fábio Augusto Reis, and João Victor Issler. "TESTING CONSUMPTION OPTIMALITY USING AGGREGATE DATA." Macroeconomic Dynamics 21, no. 5 (2016): 1119–40. http://dx.doi.org/10.1017/s1365100515000085.

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This paper tests the optimality of consumption decisions at the aggregate level, taking into account popular deviations from the canonical constant-relative-risk-aversion (CRRA) utility function model—rule of thumb and habit. First, we provide extensive empirical evidence of the inappropriateness of linearization and testing strategies using Euler equations for consumption—a drawback for standard rule-of-thumb tests. Second, we propose a novel approach to testing for consumption optimality in this context: nonlinear estimation coupled with return aggregation, where rule-of-thumb behavior and habit are special cases of an all-encompassing model. We estimated 48 Euler equations using GMM. At the 5% level, we only rejected optimality twice out of 48 times. Moreover, out of 24 regressions, we found the rule-of-thumb parameter to be statistically significant only twice. Hence, lack of optimality in consumption decisions represent the exception, not the rule. Finally, we found the habit parameter to be statistically significant on four occasions out of 24.

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Chakroun, Fatma, and Fathi Abid. "Optimal CAR simulation." International Journal of Financial Engineering 02, no. 04 (2015): 1550035. http://dx.doi.org/10.1142/s2424786315500358.

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The present paper is conceived to expose a new model of bank capital adequacy. Our analysis highly relies on the dynamics of the capital adequacy ratio (CAR) as computed from balance sheet items, namely, loans, securities and bank regulatory capital, in a stochastic dynamic setting. In addition, an attempt is made to demonstrate how the CAR can be optimized in terms of asset allocation and the rate at which the bank remains solvent. Consequently, a dynamic programming principle has been applied to solve the Hamilton–Jacobi–Bellman (HJB) equation explicitly in the case of CRRA utility function. The parameters’ estimation is based on the maximum likelihood method, using Tunisian data relevant to the period 2004–2012. As regard computations, they are carried out in MATLAB. The simulation results have shown the model relevance as a decision tool for bank risk management. Moreover, the relationship persisting between the macroeconomic activity and the bank capital adequacy has also been discussed.

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Nguyen, Manh-Hung, and Phu Nguyen-Van. "OPTIMAL ENDOGENOUS GROWTH WITH NATURAL RESOURCES: THEORY AND EVIDENCE." Macroeconomic Dynamics 20, no. 8 (2016): 2173–209. http://dx.doi.org/10.1017/s1365100515000061.

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This paper considers an optimal endogenous growth model where the production function is assumed to exhibit increasing returns to scale and two types of resource (renewable and nonrenewable) are imperfect substitutes. Natural resources, labor, and physical capital are used in the final goods sector and in the accumulation of knowledge. Based on results in the calculus of variations, a direct proof of the existence of an optimal solution is provided. Analytical solutions for the planner case, balanced growth paths, and steady states are found for a specific CRRA utility and Cobb–Douglas production function. It is possible to have long-run growth where both energy resources are used simultaneously along the equilibrium path. As the law of motion of the technological change is not concave, reflecting the increasing returns to scale, so that the Arrow–Mangasarian sufficiency conditions do not apply, we provide a sufficient condition directly. Transitional dynamics to the steady state from the theoretical model are used to derive three convergence equations of output intensity growth rate, exhaustible resource growth rate, and renewable resource growth rate, which are tested based on OECD data on production and energy consumption.

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Choi, Byungwook. "Overpriced Puts Puzzle in KOSPI 200 Options Market." Journal of Derivatives and Quantitative Studies 17, no. 3 (2009): 23–65. http://dx.doi.org/10.1108/jdqs-03-2009-b0002.

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The purpose of this paper is to examine the argument that the put options traded in the exchanges are too high, compared to the asset prices based on the classical CAPM model, and thus the short position of the put option would make a significant profit from trading. In order to explore the earlier report, this paper, using the KOSPI 200 index options market price, estimates the historical rate of return on several option trading strategies such as naked option, protective put, covered call, straddle, and strangle. Secondly this paper compares the historical rates of return on the option trading strategies and Sharpe ratios with those generated by Monte-Carlo simulation and examines whether the historical option returns are inconsistent with Black-Scholes model, Jump-diffusion model, Stochastic Volatility model, or Stochastic Volatility with Jump model. Thirdly, this paper computes the optimal asset allocation ratio among the risk-free asset, risky assets, and option trading strategies in the viewpoint of rational investors who maximize the CRRA utility function. The results show that the historical returns on short position of ATM and OTM puts are too high to explain based on the classical CAPM, and the optimal allocation ratios among put, risky asset, and the risk-free asset are different from those derived using Monte-Carlo simulation.

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Krause. "Optimal Savings Taxation when Individuals Have Different CRRA Utility Functions." Annals of Economics and Statistics, no. 113/114 (2014): 207. http://dx.doi.org/10.15609/annaeconstat2009.113-114.207.

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Perera, Ryle S. "Dynamic asset allocation for a bank under CRRA and HARA framework." International Journal of Financial Engineering 02, no. 03 (2015): 1550031. http://dx.doi.org/10.1142/s2424786315500310.

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This paper analyzes an optimal investment and management strategy for a bank under constant relative risk aversion (CRRA) and hyperbolic absolute risk aversion (HARA) utility functions. We assume that the bank can invest in treasuries, stock index fund and loans, in an environment subject to stochastic interest rate and inflation uncertainty. The interest rate and the expected rate of inflation follow a correlated Ornstein–Uhlenbeck processes and the risk premia are constants. Then we consider the portfolio choice under a power utility that the bank's shareholders can maximize expected utility of wealth at a given investment horizon. Closed form solutions are obtained in a dynamic portfolio optimization model. The results indicate that the optimal proportion invested in treasuries increases while the optimal proportion invested in the loans progressively decreases with respect to time.

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Pasin, Laura, and Tiziano Vargiolu. "Optimal Portfolio for CRRA Utility Functions when Risky Assets are Exponential Additive Processes." Economic Notes 39, no. 1-2 (2010): 65–90. http://dx.doi.org/10.1111/j.1468-0300.2010.00222.x.

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GERER, JOHANNES, and GREGOR DORFLEITNER. "A NOTE ON UTILITY INDIFFERENCE PRICING." International Journal of Theoretical and Applied Finance 19, no. 06 (2016): 1650037. http://dx.doi.org/10.1142/s0219024916500370.

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Utility-based valuation methods are enjoying growing popularity among researchers as a means to overcome the challenges in contingent claim pricing posed by the many sources of market incompleteness. However, we show that under the most common utility functions (including CARA and CRRA), any realistic and actually practicable hedging strategy involving a possible short position has infinitely negative utility. We then demonstrate for utility indifference prices (and also for the related so-called utility-based (marginal) prices) how this problem leads to a severe divergence between results obtained under the assumption of continuous trading and realistic results. The combination of continuous trading and common utility functions is thus not justified in these methods, raising the question of whether and how results obtained under such assumptions could be put to real-world use.

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Zhang, Chubing, and Ximing Rong. "Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model." Discrete Dynamics in Nature and Society 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/297875.

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We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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Monin, Phillip, and Thaleia Zariphopoulou. "On the optimal wealth process in a log-normal market: Applications to risk management." Journal of Financial Engineering 01, no. 02 (2014): 1450013. http://dx.doi.org/10.1142/s2345768614500135.

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Using a stochastic representation of the optimal wealth process in the classical Merton problem, we calculate its cumulative distribution and density functions and provide bounds and monotonicity results for these quantities under general risk preferences. We also show that the optimal wealth and portfolio processes for different utility functions are related through a deterministic transformation and appropriately modified initial conditions. We analyze the value at risk (VaR) and expected shortfall (ES) of the optimal wealth process and show how each can be used to infer a constant relative risk aversion (CRRA) investor's risk aversion coefficient. Drawing analogies to the option greeks, we study the sensitivities of the optimal wealth process with respect to the cumulative excess stock return, time, and market parameters. We conclude with a study of how sensitivities of the excess return on the optimal wealth process relate to the portfolio's beta.

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Osu, Bright O., Kevin N. C. Njoku, and Ben I. Oruh. "On the Effect of Inflation and Impact of Hedging on Pension Wealth Generation Strategies under the Geometric Brownian Motion Model." Earthline Journal of Mathematical Sciences, February 3, 2019, 119–42. http://dx.doi.org/10.34198/ejms.1219.119142.

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This work investigates the effect of Inflation and the impact of hedging on the optimal investment strategies for a prospective investor in a DC pension scheme, using inflation-indexed bond and inflation-linked stock. The model used here permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The pension plan member is allowed to invest in risk-free asset (cash), and two risky assets (i.e., the inflation-indexed bond and inflation-linked stock). A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution towards the pension fund, is constructed and presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation have significant negative effect on wealth investment strategies, particularly, the RRA(w) is not constant with the investment strategy, since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategies, and also the inflation-indexed bond and inflation-linked stock has a positive damping effect (hedging) on the severe effect of inflation.

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Njoku, K. N. C., and B. O. Osu. "On the Modified Optimal Investment Strategy for Annuity Contracts under the Constant Elasticity of Variance (CEV) Model." Earthline Journal of Mathematical Sciences, January 1, 2019, 63–90. http://dx.doi.org/10.34198/ejms.1119.6390.

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In this work, the optimal pension wealth investment strategy during the decumulation phase, in a defined contribution (DC) pension scheme is constructed. The pension plan member is allowed to invest in a risk free and a risky asset, under the constant elasticity of variance (CEV) model. The explicit solution of the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions are obtained, using Legendre transform, dual theory, and change of variable methods. It is established herein that the elastic parameter, β, say, must not necessarily be equal to one (β ≠ 1). A theorem is constructed and proved on the wealth investment strategy. Observations and significant results are made and obtained, respectively in the comparison of our various utility functions and some previous results in literature.

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