金融工程研究中心学术报告:Large ranking games with diffusion control

主 讲 人:新加坡国立大学 周超副教授




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 alpha 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 else. 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.


Zhou Chao is an Associate Professor at the Department of Mathematics and Risk Management Institute, NUS. He got his PhD in Applied Mathematics from CMAP, Ecole Polytechnique. His research interests include mathematical finance, stochastic control and deep learning in finance. He is the director of the Master in Quantitative Finance Programme and the Centre for Quantitative Finance at NUS.


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