Asymptotic Evaluations of the Stability Index for a Markov Control Process with the Expected Total Discounted Reward Criterion

In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.

Optimal consumption–investment under partial information in conditionally log-Gaussian models

Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaussian diffusion models,concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula,or HJB equations.The explicit solutions to the related forward-backward equations are also given.