On time-inconsistent stochastic control in continuous time
研究了连续时间下不满足贝尔曼最优性原理的时间不一致随机控制问题，通过博弈论框架寻找纳什子博弈完美均衡，推导出扩展的HJB方程系统，并应用于线性二次调节器和Cox-Ingersoll-Ross生产经济。
Abstract In this paper, which is a continuation of the discrete-time paper (Björk and Murgoci in Finance Stoch. 18:545–592, 2004), we study a class of continuous-time stochastic control problems which, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We study these problems within a game-theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled continuous-time Markov process and a fairly general objective functional, we derive an extension of the standard Hamilton–Jacobi–Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy as well as the equilibrium value function. The main theoretical result is a verification theorem. As an application of the general theory, we study a time-inconsistent linear-quadratic regulator. We also present a study of time-inconsistency within the framework of a general equilibrium production economy of Cox–Ingersoll–Ross type (Cox et al. in Econometrica 53:363–384, 1985).