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This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the time-inconsistent stopping control problems under general multi-dimensional controlled diffusion model and propose a formal definition of their equilibriums. We show that an admissible pair $(hat{u},C)$ of control-stopping policy is equilibrium if and only if the axillary function associated to it solves the extended HJB system. We provide almost equivalent conditions to the boundary term of this extended HJB system, which is related to the celebrated smooth fitting principles. As applications of our theoretical results, we develop an investment-withdrawal decision model for time-inconsistent decision makers in infinite time horizon. We provide two concrete examples, one of which includes constant proportion investment with one side threshold withdrawal strategy as equilibrium; in another example, all strategies with constant proportion investment are proved to be irrational, no matter what the withdrawal strategy is.
In this paper we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic to tackle the theoret
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambig
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity a
This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two levels of game-theoretic reasoning intertwined. First, each player looks for an intra-personal equilibrium among her curr
This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis to compare