Portfolio optimization of credit swap under funding costs

Lijun Bo

doi:10.1186/s41546-017-0023-6

Article Contents

2017, Volume 2: 12. Doi: 10.1186/s41546-017-0023-6

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Portfolio optimization of credit swap under funding costs

Lijun Bo^1,2, ,

1 School of Mathematics and Statistics, Xidian University, Xian 710071, China;
2 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui Province 230026, China

Lijun Bo, lijunbo@ustc.edu.cn

Received: January 27, 2017

Revised: October 17, 2017

Published: September 2020

The research was partially supported by NSF of China (No. 11471254), The Key Research Program of Frontier Sciences, CAS (No. QYZDB-SSWSYS009) and Fundamental Research Funds for the Central Universities (No. WK3470000008).

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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 Lipschitzcontinuity of the optimal strategy, we establish existence and uniqueness of a global solution to the HJB equation.

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