Spectral Decomposition of Optimal Asset-Liability Management

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: 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