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.

中文翻译：

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融资成本下信用互换的投资组合优化

我们开发了一个动态优化框架，以评估融资成本对信用掉期投资的影响。违约投资者可以购买CDS预付款，根据其信用质量以一定的利率借款，并投资于货币市场帐户。通过查看财富过程的凹漂移作为受理策略的连续函数，我们表征最优策略中的一个关键的借贷阈值和的一阶条件适当选择的系统的两种溶液之间的关系的方面。风险投资者与参考实体之间的传染效应使最优策略与控制问题的价值函数结合在一起。使用动态规划原理，我们证明了后者可以作为非线性HJB方程的解而恢复，该方程的系数允许奇异增长。