References & Citations
Quantitative Finance > Mathematical Finance
Title: Time-inconsistent mean field and n-agent games under relative performance criteria
(Submitted on 22 Dec 2023 (v1), last revised 27 Apr 2024 (this version, v2))
Abstract: In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the relative wealth and consumption to her competitors. Due to the presence of a non-exponential discount factor, each agent's optimal strategy becomes time-inconsistent. In order to resolve time-inconsistency, each agent makes a decision in a sophisticated way, choosing open-loop equilibrium strategy in response to the strategies of all the other agents. We construct explicit solutions for the $n$-agent games and the corresponding mean field games (MFGs) where the limit of former yields the latter. This solution is unique in a special class of equilibria.
Submission history
From: Keyu Zhang [view email][v1] Fri, 22 Dec 2023 05:01:17 GMT (134kb,D)
[v2] Sat, 27 Apr 2024 09:09:12 GMT (133kb,D)
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