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

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  • Zhu, Yichen
  • Escobar-Anel, Marcos

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).

Suggested Citation

  • Zhu, Yichen & Escobar-Anel, Marcos, 2022. "Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s009630032100919x
    DOI: 10.1016/j.amc.2021.126836
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