2009/03/05 by Ying Jiao, Huyên Pham, Jiao, Ying +2 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Credit Risk and Financial Regulations #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.0903.0909
arxiv created 2009/03/05 · openalex publication_date 2009/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a financial market with a stock exposed to a counterparty risk inducing a drop in the price, and which can still be traded after this default time. We use a default-density modeling approach, and address in this incomplete market context the expected utility maximization from terminal wealth. We show how this problem can be suitably decomposed in two optimization problems in complete market framework: an after-default utility maximization and a global before-default optimization problem involving the former one. These two optimization problems are solved explicitly, respectively by duality and dynamic programming approaches, and provide a fine understanding of the optimal strategy. We give some numerical results illustrating the impact of counterparty risk and the loss given default on optimal trading strategies, in particular with respect to the Merton portfolio selection problem.