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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Verfasserangaben: M. Krekel urn:nbn:de:hbz:386-kluedo-12953 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (32) Bericht Englisch 2002 2002 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 02.02.2004 HJB equation; Portfolio optimisation; credit spread; log utility; non-linear wealth dynamics; power utility; stochastic control Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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