Pricing and Portfolio Optimization Analysis in Defaultable Regime-Switching Markets

We analyze pricing and portfolio optimization problems in defaultable regime switching markets driven by a underlying continuous-time Markov process. We contribute to both of these problems by obtaining new representations of option prices and optimal portfolio strategies under regime-switching. Using our option price representation, we develop a novel efficient method to price claims which may depend on the full path of the underlying Markov chain. This is done via a change of probability measure and a short-time asymptotic expansion of the claim’ s price in terms of the Laplace transforms of the symmetric Dirichlet distribution. The proposed approach is applied to price not only simple European claims such as defaultable bonds, but also a new type of path-dependent claims that we term self-decomposable as well as the important class of vulnerable call and put options on a stock. In the portfolio optimization context, we obtain explicit constructions of value functions and investment strategies for investors with Constant Relative Risk Aversion (CRRA) utilities, built on the Hamilton-Jacobi-Bellman (HJB) framework developed in Capponi and Figueroa-López (2011). We give a precise characterization of the investment strategies in terms of corporate bond returns, forward rates, and expected recovery at default, and illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economical analysis. AMS 2000 subject classifications: 93E20, 60J20.