Relevant bibliographies by topics / Constant relative risk aversion utility function (CRRA)

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Academic literature on the topic 'Constant relative risk aversion utility function (CRRA)'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Constant relative risk aversion utility function (CRRA)"

1

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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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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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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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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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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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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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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8

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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9

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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Levy, Haim, and Moshe Levy. "Prospect theory, constant relative risk aversion, and the investment horizon." PLOS ONE 16, no. 4 (2021): e0248904. http://dx.doi.org/10.1371/journal.pone.0248904.

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Prospect Theory (PT) and Constant-Relative-Risk-Aversion (CRRA) preferences have clear-cut and very different implications for the optimal asset allocation between a riskless asset and a risky stock as a function of the investment horizon. While CRRA implies that the optimal allocation is independent of the horizon, we show that PT implies a dramatic and discontinuous “jump” in the optimal allocation as the horizon increases. We experimentally test these predictions at the individual level. We find rather strong support for CRRA, but very little support for PT.
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Books on the topic "Constant relative risk aversion utility function (CRRA)"

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Back, Kerry E. Utility and Risk Aversion. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0001.

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Expected utility is introduced. Risk aversion and its equivalence with concavity of the utility function (Jensen’s inequality) are explained. The concepts of relative risk aversion, absolute risk aversion, and risk tolerance are introduced. Certainty equivalents are defined. Expected utility is shown to imply second‐order risk aversion. Linear risk tolerance (hyperbolic absolute risk aversion), cautiousness parameters, constant relative risk aversion, and constant absolute risk aversion are described. Decreasing absolute risk aversion is shown to imply a preference for positive skewness. Preferences for kurtosis are discussed. Conditional expectations are introduced, and the law of iterated expectations is explained. Risk averse investors are shown to dislike mean‐independent noise.
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Back, Kerry E. Representative Investors. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0007.

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There is a representative investor at any Pareto optimal competitive equilibrium. If investors have linear risk tolerance with the same cautiousness parameter, then there is a representative investor with the same utility function. When there is a representative investor, there is a factor model with the representative investor’s marginal utility of consumption as the factor. If the representative investor has constant relative risk aversion, then the risk‐free return and log equity premium can be calculated in terms of moments of aggregate consumption. The equity premium and risk‐free rate puzzles are explained. The coskewness‐cokurtosis pricing model and the Rubinstein option pricing model are derived.
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