Abstract
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.
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Kraft, H., Steffensen, M. Portfolio problems stopping at first hitting time with application to default risk. Math Meth Oper Res 63, 123–150 (2006). https://doi.org/10.1007/s00186-005-0026-4
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DOI: https://doi.org/10.1007/s00186-005-0026-4