Risk‐sensitive large‐population linear‐quadratic‐Gaussian Games with major and minor agents

Abstract

This paper studies large‐population dynamic games involving a linear‐quadratic‐Gaussian (LQG) system with an exponential cost functional. The parameter in the cost functional can describe an investor's risk attitude. In the game, there are a major agent and a population of minor agents where is very large. The agents in the games are coupled via both their individual stochastic dynamics and their individual cost functions. The mean field methodology yields a set of decentralized controls, which are shown to be an ‐Nash equilibrium for a finite population system where . Numerical results are established to illustrate the impact of the population's collective behaviors and the consistency of the mean field estimation.

A maximum principle for progressive optimal control of mean‐field forward–backward stochastic system involving random jumps and impulse controls

“…Nowadays, mean-field control and game problems have attracted and gained more and more researchers' attentions, because of the extensive applications and significant theoretical values in many fields, such as economics, information technology, engineering, and system control [1][2][3][4][5][6][7][8][9][10]. There are two typically used problem frames and models for the mean-field control.…”