论文标题
默认情况前后
Before and after default: information and optimal portfolio via anticipating calculus
论文作者
论文摘要
当风险资产受到破产的威胁时，默认风险演算在投资组合优化中起着至关重要的作用。但是，在这种情况下，传统的随机控制技术不适用，需要其他假设才能在前后默认情况下获得最佳解决方案。我们提出了一种使用正向集成的替代方法，该方法允许避免使用限制性假设之一，即jacod密度假设。我们证明，在对数实用程序的情况下，强度较弱的假设是最佳的适当条件。此外，我们在过滤中逐渐扩大以适应默认过程的危险资产的半明星分解，假设存在最佳投资组合。这项工作旨在在面对违约风险时提供有价值的见解，以制定有效的风险管理策略。
Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not applicable in this scenario, and additional assumptions are required to obtain the optimal solution in a before-and-after default context. We propose an alternative approach using forward integration, which allows to avoid one of the restrictive assumptions, the Jacod density hypothesis. We demonstrate that, in the case of logarithmic utility, the weaker intensity hypothesis is the appropriate condition for optimality. Furthermore, we establish the semimartingale decomposition of the risky asset in the filtration that is progressively enlarged to accommodate the default process, under the assumption of the existence of the optimal portfolio. This work aims to provide valueable insights for developing effective risk management strategies when facing default risk.
