A note on a new class of recursive utilities in Markov decision processes

Abstract

This paper deals with Markov decision processes on a general state space under standard compactness-continuity assumptions. The purpose is to obtain a new class of so-called recursive utilities with the aid of the entropic risk measure. Within this framework we show that there exists a stationary policy for a discounted payoff problem in the infinite time horizon. Our result is illustrated by examples.2010 Mathematics Subject Classification: Primary 90C40; Secondary 90C39, 91B70.

Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players

“…On the other hand, our result can also be viewed as an extension of the optimization problem (one player case), studied in Asienkiewicz and Jaśkiewicz (2017) and Bäuerle and Jaśkiewicz (2018), to a strategic version of a one-sector optimal growth model. In contrast to Bäuerle and Jaśkiewicz (2018), we examine, as mentioned above, a model with bounded felicity functions.…”

“…for all s ∈ S and (π, σ ) ∈ Π × Σ. The reader is referred to Asienkiewicz and Jaśkiewicz (2017), where (5) and further details are proved. Hence, lim N →∞ U i N (s, π, σ ) exists and let us denote this limit by U i (s, π, σ ).…”

“…For instance, Hansen and Sargent (1995) applied them to a linear quadratic Gaussian control model, and Weil (1993) used them to examine precautionary savings and permanent income hypothesis. Moreover, these preferences found applications in the problems of Pareto optimal allocations (Anderson 2005) as well as in the study of Markov decision processes (Asienkiewicz and Jaśkiewicz 2017) or in one-sector optimal growth model with an unbounded felicity function (Bäuerle and Jaśkiewicz (2018)) . As argued by Hansen and Sargent (1995) the preferences in (1) are also attractive, because they can viewed as the robustness preferences.…”

Optimal dividend payout model with risk sensitive preferences

“…If u is an exponential utility then we obtain in the previous case that S u is the entropic risk measure (Example 1 a)) and the optimality equation ( 9) reduces to (see Asienkiewicz and Jaśkiewicz (2017))…”

Dynamic Reinsurance in Discrete Time Minimizing the Insurer's Cost of Capital

“…The latter is a random quantity depending on the development of the future surplus. The recursive minimization of risk measures has been studied by Asienkiewicz and Jaśkiewicz (2017) for an abstract Markov Decision Process and by Jaśkiewicz (2017, 2018) for a dividend and an optimal growth problem specifically using the entropic risk measure. This choice is motivated by recursive utilities studied extensively in the economic literature since the entropic risk measure happens to be the certainty equivalent of an exponential utility.…”