Year: 2017
Type: preprint
Abstract: In this paper we explore the impact of quantiles on optimal strategies under state dynamics driven by both individual noise, common noise and Poisson jumps. We first establish an optimality system satisfied the quantile process under jump terms. We then turn to investigate a new class of finite horizon mean-field games with common noise in which the payoff functional and the state dynamics are dependent not only on the state-action pair but also on conditional quantiles. Based on the best-response of the decision-makers, it is shown that the equilibrium conditional quantile process satisfies a stochastic partial differential equation in the non-degenerate case. A closed-form expression of the quantile process is provided in a basic Ornstein-Uhlenbeck process with common noise.
Source: arXiv (Cornell University)
Author: Tembine, Hamidou
Institution: New York University Abu Dhabi
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: U.S. Air Force
Awards: G6750170684, G7090116110
OpenAlex ID: W2745360718