Portfolio Optimization with a Defaultable Security
by Tomasz R. Bielecki of the Illinois Institute of Technology, and
February 27, 2007
Abstract: In this paper we derive a closed-form solution for a representative investor who optimally allocates her wealth among the following securities: a credit-risky asset, a default-free bank account, and a stock. Although the inclusion of a credit-related financial product in the portfolio selection is more realistic, no closed-form solutions to date are given in the literature when a recovery value is considered in the event of a default. While most authors have assumed some recovery scheme in their initial model set up, they do not address the portfolio problem with a recovery when a default actually occurs. Given the tractability of the recovery of market value, we solved the optimal portfolio problem for the representative investor whose utility function is a Constant Relative Risk Aversion utility function.
Keywords: Portfolio optimization, defaultable security, credit risk, recovery of market value.
Published in: Asia-Pacific Financial Markets, Vol. 13, No. 2, (June 2006), pp. 113-127.