Speaker : Dr. Anugu Sumith Reddy,
Post Doctoral Fellow, Rice University
Date and Time : Monday, 19th August, 11.00 am- 12.00 noon
Venue: Ramanujan Hall
Title: Ergodic risk sensitive control of diffusions under a general
structural hypothesis
Abstract: In this talk, we present the ergodic (infinite horizon) risk
sensitive control (ERSC) problem for diffusion processes under a general
hypothesis that is 'in between' the conditions of uniform stability and
near-monotonicity. This problem can be studied as a limit of a family of
perturbed ERSC problems with inf-compact running cost. Because of the
exponential nature of the cost function, limiting procedure is
challenging. We discuss how we overcome this challenge. This involves
exploiting a well-known variational representation of exponential
functionals of Brownian motion and applying it to the objective
exponential cost function of the controlled diffusion. This representation
facilitates us to view the risk sensitive cost for any stationary Markov
control as the optimal value of a control problem of an extended diffusion
involving a new auxiliary control where the optimal criterion is to
maximize the associated long-run average cost criterion that is a
difference of the original running cost and an extra term that is
quadratic in the auxiliary control. The main difficulty in using this
approach lies in the fact that tightness of mean empirical measures of
the extended diffusion is not a priori implied by the analogous tightness
property of the original diffusion. We will discuss how to overcome this
by establishing a priori estimates for the extended diffusion associated
with the nearly optimal auxiliary controls. Finally, we present the
relevant results on characterization of optimal va
lue and optimal
controls.