On the relative value iteration with a risk-sensitive criterion

TL;DR

This paper introduces a multiplicative relative value iteration algorithm for risk-sensitive control problems in Markov chains and diffusions, proving its convergence in both discrete and continuous settings.

Contribution

It provides the first convergence proof of a multiplicative relative value iteration algorithm for risk-sensitive control in both discrete and continuous models.

Findings

Proves convergence of the algorithm in discrete controlled Markov chains.

Establishes convergence in controlled diffusions on Euclidean space.

Extends the applicability of relative value iteration to risk-sensitive criteria.

Abstract

A multiplicative relative value iteration algorithm for solving the dynamic programming equation for the risk-sensitive control problem is studied for discrete time controlled Markov chains with a compact Polish state space, and controlled diffusions in on the whole Euclidean space. The main result is a proof of convergence to the desired limit in each case.