We consider the problem of maximizing expected utility from terminal wealth for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observation control problem via the filtered regime switching probabilities. We separate the latter into a pre-default and a post-default dynamic optimization subproblems and obtain two coupled Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove existence and uniqueness of a globally bounded classical solution to the pre-default HJB equation and give a verification theorem characterizing each value function as the solution of the corresponding HJB equation. This is joint work with Agostino Capponi and Andrea Pascucci.

Prof.  Figueroa-Lopez  received a BS in applied mathematics in 1995 from the Universidad Autonoma Metropolitan in Mexico City, an  MA in Statistics from CIMAT-Univesidad de Guanajuato in 1888, an MS in Quantitative and Computational Finance from Georgia Tech in 2002 and a PhD in Applied Mathematics from Georgia Tech in 2004. He was at Purdue from 2004 until 2015 when he went to Washington University in St. Louis as a tenured Associate Professor.  He is now a full professor in the Department of Mathematics and Statistics at Washington University.