Vanishing discount approximations in controlled Markov chains with risk-sensitive average criterion. (20th March 2018)

• Record Type: Journal Article
• Authors: Cavazos-Cadena, Rolando; Hernández-Hernández, Daniel
• Is Part Of: Advances in applied probability. Volume 50:Number 1(2018)
• Page Start: 204
• Page End: 230
• Publication Date: 2018-03-20
• Subjects: Exponential utility, -- certainty equivalent, -- vanishing discount method, -- Hölder's inequality, -- convex function; Primary 60J19, -- Secondary 90C39; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2018.10
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: This work concerns Markov decision chains on a finite state space. The decision-maker has a constant and nonnull risk sensitivity coefficient, and the performance of a control policy is measured by two different indices, namely, the discounted and average criteria. Motivated by well-known results for the risk-neutral case, the problem of approximating the optimal risk-sensitive average cost in terms of the optimal risk-sensitive discounted value functions is addressed. Under suitable communication assumptions, it is shown that, as the discount factor increases to 1, appropriate normalizations of the optimal discounted value functions converge to the optimal average cost, and to the functional part of the solution of the risk-sensitive average cost optimality equation.