This paper deals with denumerable discrete-time Markov decision processes with unbounded costs. The criteria to be minimized are both of the limsup and liminf average criteria, instead of only the limsup average criterion widely used in the previous literature. We give another set of conditions...

In this paper we consider the convergence of a sequence {Mn} of the models of discounted continuous-time constrained Markov decision processes (MDP) to the “limit” one, denoted by M∞. For the models with denumerable states and unbounded transition rates, under reasonably mild conditions we...

In this paper, we study constrained continuous-time Markov decision processes with a denumerable state space and unbounded reward/cost and transition rates. The criterion to be maximized is the expected average reward, and a constraint is imposed on an expected average cost. We give suitable...

. In this paper, we consider the nonstationary Markov decision processes (MDP, for short) with average variance criterion on a countable state space, finite action spaces and bounded one-step rewards. From the optimality equations which are provided in this paper, we translate the average...

This paper is devoted to studying continuous-time Markov decision processes with general state and action spaces, under the long-run expected average reward criterion. The transition rates of the underlying continuous-time Markov processes are allowed to be unbounded, and the reward rates may...

This paper deals with denumerable discrete-time Markov decision processes with unbounded costs. The criteria to be minimized are both of the limsup and liminf average criteria, instead of only the limsup average criterion widely used in the previous literature. We give another set of conditions...

This paper deals with a new optimality criterion consisting of the usual three average criteria and the canonical triplet (totally so-called strong average-canonical optimality criterion) and introduces the concept of a strong average-canonical policy for nonstationary Markov decision processes,...

In this paper, we consider discrete-time <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation>-person constrained stochastic games with discounted cost criteria. The state space is denumerable and the action space is a Borel set, while the cost functions are admitted to be unbounded from below and above. Under suitable conditions...</equationsource></equationsource></inlineequation>

The optimal excess-of-loss reinsurance and investment strategies under a constant elasticity of variance (CEV) model for an insurer are considered in this paper. Assume that the insurer’s surplus process is approximated by a Brownian motion with drift, the insurer can purchase excess-of-loss...

In this paper, we consider a mean–variance optimization problem for Markov decision processes (MDPs) over the set of (deterministic stationary) policies. Different from the usual formulation in MDPs, we aim to obtain the mean–variance optimal policy that minimizes the variance over a set of...