On time-inconsistent stochastic control in continuous time
On time-inconsistent stochastic control in continuous time
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DOI：
10.1007/s00780-017-0327-5
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发表时间：
2017-04-01
影响因子：
1.7
通讯作者：
Murgoci, Agatha
中科院分区：
文献类型：
--
作者：
Bjork, Tomas;Khapko, Mariana;Murgoci, Agatha
在本文中，这是一个连续的离散时间文件（比约克和Murgoci在金融Stoch。18：545-592，2004），我们研究了一类连续时间随机控制问题，这些问题在不同的方面都是时间不一致的，因为它们不承认Bellman最优性原理。我们研究这些问题的博弈论框架内，我们寻找纳什子博弈完美均衡点。对于一般受控连续时间马尔可夫过程和一个相当一般的目标泛函，我们导出了标准Hamilton-Jacobi-Bellman方程的一个扩展，以非线性方程组的形式，用于确定平衡策略以及平衡值函数。主要的理论结果是一个验证定理。作为一般理论的应用，我们研究了时间不一致线性二次型调节器。我们还在Cox-Ingersoll-Ross型一般均衡生产经济的框架内对时间不一致性进行了研究（考克斯等人，《计量经济学》53：363-384，1985）。
In this paper, which is a continuation of the discrete-time paper (Bjork 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).