Portfolio optimization of credit swap under funding costs

• Main Author: Lijun Bo
• Format: Article
• Language: English
• Published: SpringerOpen 2017-12-01
• Series: Probability, Uncertainty and Quantitative Risk
• Online Access: http://link.springer.com/article/10.1186/s41546-017-0023-6

Abstract We develop a dynamic optimization framework to assess the impact of funding costs on credit swap investments. A defaultable investor can purchase CDS upfronts, borrow at a rate depending on her credit quality, and invest in the money market account. By viewing the concave drift of the wealth process as a continuous function of admissible strategies, we characterize the optimal strategy in terms of a relation between a critical borrowing threshold and two solutions of a suitably chosen system of first order conditions. Contagion effects between risky investor and reference entity make the optimal strategy coupled with the value function of the control problem. Using the dynamic programming principle, we show that the latter can be recovered as the solution of a nonlinear HJB equation whose coeffcients admit singular growth. By means of a truncation technique relying on the locally Lipschitz-continuity of the optimal strategy, we establish existence and uniqueness of a global solution to the HJB equation.