Faculty of Economics and Business Administration Publications Database

Portfolio Problems Stopping at First Hitting Time with Application to Default Risk

Steffensen, Mogens
Volume: 63
Number: 1
Pages: 123 - 150
Month: February
Link External Source: Online Version
Year: 2006
Keywords: Optimal Consumption and Investment; Random Time Horizon; Feynman-Kac Representation; Barrier Options

In this paper a portfolio problem is considered where trading in the risky asset is stopped if a state process hits a predefined barrier. This state process need not to be perfectly correlated with the risky asset. We give a representation result for the value function and provide a verification theorem. As an application, we explicitly solve the problem by assuming that the state process is an arithmetic Brownian motion. Then the result is used as a starting point to solve and analyze a portfolio problem with default risk modeled by the Black-Cox approach. Finally, we discuss how our results can be applied to a portfolio problem with stochastic interest rates and default risk modeled by the approach of Briys and de Varenne.