存在违约风险时股票与信用违约互换的最优投资
Optimal Investment in Equity and Credit Default Swaps in the Presence of Default
AI总结：
本文研究存在违约风险时股票与信用违约互换（CDS）市场的最优投资问题，通过求解具有二次增长的半线性PDE刻画确定性等价，证明最优CDS策略覆盖违约损失及未来交易机会受限损失，并表明该策略本质上是静态的且能显著提升投资者效用。
摘要：
我们考虑一个同时面临不可对冲冲击风险和违约风险的股票市场。本文的创新之处在于，为了部分抵消违约风险，投资者可以在信用违约互换（CDS）市场中进行动态交易。假设投资机会由一个基础扩散因子过程的函数驱动，我们为具有常数绝对风险厌恶系数的投资者识别出其确定性等价，该确定性等价由一个半线性偏微分方程（PDE）刻画，该方程在函数系数和梯度系数上均具有二次增长。对于一般模型设定，我们证明了该PDE解的存在性，且该解即为确定性等价。我们表明，CDS市场中的最优策略不仅覆盖违约时的股票损失（正如人们所预期的那样），还覆盖因未来交易机会受限而产生的损失。我们利用所得结果，通过效用无差异原则为依赖违约的未定权益定价，并证明只要基础股票市场在不存在违约可能性的情况下是完备的，那么考虑违约后的股票-CDS市场也是完备的。最后，通过数值应用，我们表明最优CDS策略本质上是静态的（因此易于实施），并且投资CDS能显著提高投资者的间接效用。
英文摘要：
We consider an equity market subject to risk from both unhedgeable shocks and default. The novelty of our work is that to partially offset default risk, investors may dynamically trade in a credit default swap (CDS) market. Assuming investment opportunities are driven by functions of an underlying diffusive factor process, we identify the certainty equivalent for a constant absolute risk aversion investor with a semi-linear partial differential equation (PDE) which has quadratic growth in both the function and gradient coefficients. For general model specifications, we prove existence of a solution to the PDE which is also the certainty equivalent. We show the optimal policy in the CDS market covers not only equity losses upon default (as one would expect), but also losses due to restricted future trading opportunities. We use our results to price default dependent claims though the principal of utility indifference, and we show that provided the underlying equity market is complete absent the possibility of default, the equity-CDS market is complete accounting for default. Lastly, through a numerical application, we show the optimal CDS policies are essentially static (and hence easily implementable) and that investing in CDS dramatically increases investor indirect utility.
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