Spectral Decomposition of Optimal Asset-Liability Management

21 Pages Posted: 6 Oct 2008 Last revised: 16 Mar 2009

See all articles by Ann De Schepper

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Marc Decamps

Katholieke Universiteit Leuven (KUL)

Date Written: January 31, 2008

Abstract

This paper concerns optimal asset-liability management when the assets and the liabilities are modeled by means of correlated geometric Brownian motions as suggested in Gerber and Shiu (2003). In a first part, we apply singular stochastic control techniques to derive a free boundary equation for the optimal value creation as a growth of liabilities or as dividend payment to shareholders. We provide analytical solutions to the HJB optimality equation in a rather general context. In a second part, we study the convergence of the cash flows to the optimal value creation using spectral methods. For particular cases, we also provide a series expansion for the probabilities of bankruptcy in finite time.

Keywords: asset-liability management, HJB principle, local time, spectral theory

Suggested Citation

De Schepper, Ann and Goovaerts, Marc and Decamps, Marc, Spectral Decomposition of Optimal Asset-Liability Management (January 31, 2008). Journal of Economic Dynamics and Control, Vol. 33, No. 3, pp. 710-724, 2009, Available at SSRN: https://ssrn.com/abstract=1279224

Ann De Schepper

University of Antwerp - Faculty of Applied Economics ( email )

Prinsstraat 13
Antwerp, B-2000
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Marc Decamps (Contact Author)

Katholieke Universiteit Leuven (KUL) ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

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