Portfolio optimization of credit swap under funding costs

Abstract

which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. AbstractWe 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.

Binary funding impacts in derivative valuation

“…However, under clean price , still exists even when . This is one of the reasons why replacement cost should be discussed. (v)Considering different lending/borrowing not only makes the BSDEs for replication pricing semilinear, but also makes the associated Hamiltonians nonsmooth in optimal investment problems (see Bo, 2017; Bo & Capponi, 2016; Yang, Liang, & Zhou, 2019, for examples).…”

A Risk-Sharing Framework of Bilateral Contracts

“…One mathematical difficulty to deal with the risk-sharing problem is that the amount by breach of contract is given by piece-wise concave functions. Mathematically similar problems were solved by [24,15,14,51]. In [24], portfolio optimization problems were considered where the agent switches utilities.…”

“…They used duality method that cannot be applied to our problem as we cannot impose a positive constraint for the portfolio. In [15,14], the piece-wise concave property arose from different lending/borrowing rates and they solved the optimization problem by using HJB equations. In their problem, the associated HJB equations had a homothetic property.…”