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arXiv · 1909.06863

Time-inconsistent Risk-sensitive Equilibrium for Countable-stated Markov Decision Processes

Hongwei Mei
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Abstract

This paper is devoted to solving a time-inconsistent risk-sensitive control problem with parameter $\e$ and its limit case ($\e\rightarrow0^+$) for countable-stated Markov decision processes (MDPs for short). Since the cost functional is time-inconsistent, it is impossible to find a global optimal strategy for both cases. Instead, for each case, we will prove the existence of time-inconstant equilibrium strategies which verify the so-called step-optimality. Moreover, we prove the convergence of $\e$-equilibriums and the corresponding value functions as $\e\rightarrow0^+$.

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Hongwei Mei. 2020-10-21. Time-inconsistent Risk-sensitive Equilibrium for Countable-stated Markov Decision Processes. https://arxiv.org/abs/1909.06863

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