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Mathematical Methods of Operations Research

, Volume 63, Issue 1, pp 123–150 | Cite as

Portfolio problems stopping at first hitting time with application to default risk

  • Holger KraftEmail author
  • Mogens Steffensen
Original Article

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.

Keywords

Optimal consumption and investment Random time horizon Feynman-Kac representation Barrier options 

JEL Classification

G11 

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany

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