Forward utility and market adjustments in relative investment-consumption games of many players

Abstract

We study a portfolio management problem featuring many-player and mean field competition, investment and consumption, and relative performance concerns under the forward performance processes (FPP) framework. We focus on agents using power (CRRA) type FPPs for their investment-consumption optimisation problem an under common noise Merton market model and we solve both the many-player and mean field game providing closed-form expressions for the solutions where the limit of the former yields the latter.In our case, the FPP framework yields a continuum of solutions for the consumption component as indexed to a market parameter we coin "market consumption intensity". The parameter permits the agent to set a preference for their consumption going forward in time that, in the competition case, reflects a common market behaviour. We show the FPP framework, under both competition and no-competition, allows the agent to disentangle his risk-tolerance and elasticity of intertemporal substitution (EIS) just like Epstein-Zin preferences under recursive utility framework and unlike the classical utility theory one. This, in turn, allows a finer analysis on the agent's consumption "income" and "substitution" regimes, and, of independent interest, motivates a new strand of economics research on EIS under the FPP framework.We find that competition rescales the agent's perception of consumption in a non-trivial manner in addition to a time-dependent elasticity of conformity of the agent to the market's consumption intensity.

Mean Field Portfolio Games

“…(1. 7) In (1.6), π is the amount of money invested in the risky asset while π in (1.7) is the fraction of money invested in the risky asset. In MFGs (1.6) and (1.7), by the approach introduced in [18,22], we only need to consider a representative player's utility maximization problem with µ fixed, which in turn should be consistent with the aggregation of the optimal wealth.…”

“…In addition to [21], many player portfolio games with mean field interaction have been studied in [6,7,8,9,16,20], where in [6,7] Reis and Platonov studied many player games with forward utilities, in [20] Lacker and Soret extended the CRRA model in [21] to include consumption, by using PDE approaches. In [16] Hu and Zariphopoulou studied the many player games in Itô-diffusion environment.…”