Optimal Investment with Counterparty Risk: A default-density modeling approach

by Ying Jiao of Université Paris 7, and
Huyên Pham of Université Paris 7 & Institut Universitaire de France

March 3, 2009

Abstract: 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 nd the loss given default on optimal trading strategies, in particular with respect to the Merton portfolio selection problem.

JEL Classification: G1, G11.

Keywords: Counterparty risk, density of default time, optimal investment, duality, dynamic programming, backward stochastic differential equation.

Forthcoming in: Finance and Stochastics.

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