Related papers: Optimal stopping problems with regime switching: a…
We adapt the Stochastic Perron's method in Bayraktar and Sirbu (ArXiv: 1103.0538) to the case of double obstacle problems associated to Dynkin games. We construct, symmetrically, a viscosity sub-solution which dominates the upper value of…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
In this work, we outline the entropy viscosity method and discuss how the choice of scaling influences the size of viscosity for a simple shock problem. We present examples to illustrate the performance of the entropy viscosity method under…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward…
We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
Recently, there has been a surge in interest in safe and robust techniques within reinforcement learning (RL). Current notions of risk in RL fail to capture the potential for systemic failures such as abrupt stoppages from system failures…
In this paper, we consider the problem of pollution control in a system that undergoes regular regime shifts. We first show that the optimal policy of pollution abatement is periodic as well, and is described by the unique hybrid limit…
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We…
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…
This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…