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

30 Pages Posted: 3 Aug 2004

See all articles by Mogens Steffensen

Mogens Steffensen

University of Copenhagen

Holger Kraft

Goethe University Frankfurt

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.

Suggested Citation

Steffensen, Mogens and Kraft, Holger, Portfolio Problems Stopping at First Hitting Time with Application to Default Risk (January 21, 2004). Available at SSRN: https://ssrn.com/abstract=565321 or http://dx.doi.org/10.2139/ssrn.565321

Mogens Steffensen

University of Copenhagen ( email )

Universitetsparken 5
DK-2100 Copenhagen
Denmark

Holger Kraft (Contact Author)

Goethe University Frankfurt ( email )

Faculty of Economics and Business
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany