Portfolio optimization with a defaultable security |
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Authors: | Tomasz R. Bielecki Inwon Jang |
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Affiliation: | (1) Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Street, Chicago, IL 60616, USA;(2) Department of Accounting and Finance, Merrimack College, 315 Turnpike Street, North Andover, MA 01845, USA |
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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. We find that the investor will allocate larger fraction of wealth to the defaultable security as long as the default-event risk is priced. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities. |
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Keywords: | Portfolio optimization Defaultable security Credit risk Recovery of market value |
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