Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models

Yichen Zhu and Marcos Escobar-Anel
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: This paper designs a numerical methodology, named PAMH, to approximate an investor’s optimal portfolio strategy in the contexts of expected utility theory (EUT) and mean-variance theory (MVT). Thanks to the use of hyperbolic absolute risk aversion utilities (HARA), the approach produces optimal solutions for decreasing relative risk aversion (DRRA) investors, as well as for increasing relative risk aversion (IRRA) agents. The accuracy and efficiency of the approximation is examined in a comparison to known closed-form solutions for a one dimensional (n=1) geometric Brownian motion with a CIR stochastic volatility model (i.e. GBM 1/2 or Heston model), and a high dimensional (up to n=35) stochastic covariance model. The former confirms the method works even when the theoretical candidate is not well-defined, while the latter illustrates low errors (up to 8% in certainty equivalent rate (CER)) and feasible computational time (less than one hour in a PC).

Keywords: Dynamic programming; Quadratic-affine processes; Expected utility; Portfolio optimization; 4/2 stochastic volatility (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s009630032100919x

DOI: 10.1016/j.amc.2021.126836

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