2022/07/05 by José Antonio Salmerón, Salmerón, José A., Giulia Di Nunno +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #60G44 #60H0 #93E20 #Credit Risk and Financial Regulations #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2208.07163
openalex publication_date 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.