Related papers: Conditional Optimal Stopping: A Time-Inconsistent …
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for…
This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time.…
We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…
We study a class of infinite-horizon impulse control problems with execution delay in discrete time. Using probabilistic methods, particularly the notion of the Snell envelope of processes, we construct an optimal strategy among all…
For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated…
We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…
Autonomous control systems use various sensors to decrease the amount of uncertainty under which they operate. While providing partial observation of the current state of the system, sensors require resources such as energy, time and…
Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…