Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time

Time Inconsistent Stochastic Control in Continuous Time: Theory

In this paper, which is a continuation of the discrete time paper [4], we develop a theory for 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 con...

Time-Inconsistent Stochastic Linear-Quadratic Control

Abstract. In this paper, we formulate a general time-inconsistent stochastic linear–quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition...

Stochastic Control in Continuous Time

Idempotent Expansions for Continuous-Time Stochastic Control

It is now well-known that many classes of deterministic control problems may be solved by max-plus or minplus (more generally, idempotent) numerical methods. These methods include max-plus basis-expansion approaches [1], [2], [6], [9], as well as the more recently developed curseof-dimensionality-free methods [9], [14]. It has recently been discovered that idempotent methods are applicable to s...

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.