Related papers: Optimal Equilibria for Multi-dimensional Time-inco…
We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…
Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…
This paper presents a new condition for the existence of optimal stationary policies in average-cost continuous-time Markov decision processes with unbounded cost and transition rates, arising from controlled queueing systems. This…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
We consider an optimal stopping time problem related with many models found in real options problems. The main goal of this work is to bring for the field of real options, different and more realistic pay-off functions, and negative…
We consider the problem of computing the value and an optimal strategy for minimizing the expected termination time in one-counter Markov decision processes. Since the value may be irrational and an optimal strategy may be rather…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
In this paper, we consider a general time-inconsistent optimal control problem for a non homogeneous linear system, in which its state evolves according to a stochastic differential equation with deterministic coefficients, when the noise…
We study optimal stopping of Feller-Markov processes to maximise an undiscounted functional consisting of running and terminal rewards. In a finite-time horizon setting, we extend classical results to unbounded rewards. In infinite horizon,…
We consider synthesis of control policies that maximize the probability of satisfying given temporal logic specifications in unknown, stochastic environments. We model the interaction between the system and its environment as a Markov…
Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…
Autonomous systems often have logical constraints arising, for example, from safety, operational, or regulatory requirements. Such constraints can be expressed using temporal logic specifications. The system state is often partially…
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…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We…
In this paper, we propose a novel equilibrium solution notion for the time-inconsistent stochastic linear-quadratic optimal control problem. This notion is called the mixed equilibrium solution, which consists of two parts: a…