Portfolio Problems Stopping at First Hitting Time with Application to Default Risk
30 Pages Posted: 3 Aug 2004
Date Written: January 21, 2004
Abstract
In this paper a portfolio problem is considered where trading in the risky asset is stopped if some 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.
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