Optimal Portfolios With A Loan Dependent Credit Spread

  • If an investor borrows money he generally has to pay higher interest rates than he would have received, if he had put his funds on a savings account. The classical model of continuous time portfolio optimisation ignores this effect. Since there is obviously a connection between the default probability and the total percentage of wealth, which the investor is in debt, we study portfolio optimisation with a control dependent interest rate. Assuming a logarithmic and a power utility function, respectively, we prove explicit formulae of the optimal control.

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Author:M. Krekel
URN (permanent link):urn:nbn:de:hbz:386-kluedo-12953
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (32)
Document Type:Report
Language of publication:English
Year of Completion:2002
Year of Publication:2002
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2004/02/02
Tag:HJB equation; Portfolio optimisation; credit spread; log utility; non-linear wealth dynamics; power utility; stochastic control
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011