Asymptotic analysis of the expected utility maximization problem with respect to perturbations of the numeraire

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Mostovyi, Oleksii¹ 

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

关键词: Sensitivity analysis;    Utility maximization;    Semimartingale characteristics;    Sherman-Morrison formula;    Envelope theorem;    Numeraire;   

DOI  :  10.1016/j.spa.2020.01.003

来源: Elsevier

【 摘 要 】

In an incomplete model, where under an appropriate numeraire, the stock price process is driven by a sigma-bounded semimartingale, we investigate the behavior of the expected utility maximization problem under small perturbations of the numeraire. We establish a quadratic approximation of the value function and a first-order expansion of the terminal wealth. Relying on a description of the base return process in terms of its semimartingale characteristics, we also construct wealth processes and nearly optimal strategies that allow for matching the primal value function up to the second order. We also link perturbations of the numeraire to distortions of the finite-variation part and martingale part of the stock price return and characterize the asymptotic expansions in terms of the risk-tolerance wealth process. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free