Dynamic portfolio optimization with credit risk

Abstract

Credit risk, which considers the risk of loss resulting from a counterparty's failure to meet contractual obligations, was not properly studied in the literature of dynamic portfolio optimization problem until the 2008-2009 financial crisis. This thesis is devoted to the dynamic portfolio optimization with credit risk. Two main topics are studied in this thesis. In the first topic, we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and other companies, and the default of the company induces immediate drops in the stock prices of the surviving companies. Under such looping contagion risk framework, we prove that the value function is the unique viscosity solution of the HJB equation. We also perform some numerical tests to compare and analyse the statistical distributions of the terminal wealth of log utility and power utility based on two strategies, one using the full information of intensity process and the other a proxy constant intensity process. The numerical tests confirm that modeling looping contagion risk properly is important, especially in financial distressed period. The second topic is on dynamic portfolio optimization with contingent convertible (CoCo) bond. As a new type of hybrid product, CoCo bond has the interesting feature that converting from debt to equity is contingent. We model the conversion of CoCo bond by reduced-form approach and assume that the conversion intensity is a deterministic function of the coupon rate and the issuing bank's stock price. Theoretically, we construct the viscosity solution representation between the value function and the corresponding HJB equation. Practically, we compare the performance between investing into CoCo bond and the issuing bank's stock. We analyse the statistical distributions of terminal wealth of log utility and power utility based on these two investment choices. Our simulation results show that, the CoCo bond holders bear more loss than equity holders if conversion occurs. However, investing into CoCo bond gets more profit (mean) while bearing less market risk (volatility) as long as conversion does not occur.