 Optimal portfolio with relative performance and CRRA risk preferences in a partially observable financial marketPanpan Zhang and Zhiguo Yan Applied Mathematics and Computation, 2024, vol. 481, issue C Abstract: We study a class of optimal portfolio problems with relative performance and constant relative risk aversion (CRRA) risk preferences in a partially observable financial market. The price of a stock is described by a factor model and agents (investors or fund managers) make use of stock price data to estimate the factor process. All agents have CRRA (power or logarithmic) utility functions and they all want to maximize their utilities of above-average wealth and average wealth is the geometric mean of the overall wealth. We use a competition weight to control the tradeoff between absolute and relative performance. We consider both an n-agent game and the corresponding mean field game (MFG). For the finite population game, we give a linear feedback Nash equilibrium. For the MFG, we obtain a linear feedback mean field equilibrium (MFE). Our results show that the limiting strategy for the finite population game can be derived as equilibrium of suitable MFG for CRRA case in a partially observable financial market. Keywords: Optimal portfolio; Relative performance; CRRA risk preferences; Partial information; Nash equilibrium; Mean field equilibrium (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004089 DOI: 10.1016/j.amc.2024.128947 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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