第75回研究会

開催日：

2023年3月13日(月) 17:00-18:00

会場：

Webinar形式 (Zoom)

報告者：

Chao Zhou 氏 (Associate Professor, National University of Singapore)

タイトル：

Large ranking games with diffusion control

概要Overview

We consider a symmetric stochastic differential game where each player can control the diffusion intensity of an individual dynamic state process, and the players whose states at a deterministic finite time horizon are among the best of all states receive a fixed prize. Within the mean field limit version of the game we compute an explicit equilibrium, a threshold strategy that consists in choosing the maximal fluctuation intensity when the state is below a given threshold, and the minimal intensity otherwise. We show that for large n the symmetric n-tuple of the threshold strategy provides an approximate Nash equilibrium of the n-player game. We also derive the rate at which the approximate equilibrium reward and the best response reward converge to each other, as the number of players n tends to infinity. Finally, we compare the approximate equilibrium for large games with the equilibrium of the two-player case. This talk is based on the joint work with Stefan Ankirchner, Nabil Kazi-Tani and Julian Wendt.

講師ご略歴Profile for speakers

Chao ZHOU is an Associate Professor in the Department of Mathematics and the Risk Management Institute at National University of Singapore (NUS). He serves currently as the Director of the Centre for Quantitative Finance and the MSc in Quantitative Finance Programme at NUS. He received the Ph.D. degree in Applied Mathematics from the École Polytechnique in 2012. Chao ZHOU’s research interests include stochastic control and model uncertainty in quantitative finance. He has published papers in leading journals such as Annals of Probability, Annals of Applied Probability, Mathematical Finance and Journal of Computational Physics. He is serving as Associate Editor for Mathematics and Financial Economics.

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