Spectral decomposition of optimal asset-liability management

Marc Decamps, Ann De Schepper () and Marc Goovaerts

Journal of Economic Dynamics and Control, 2009, vol. 33, issue 3, 710-724

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. Geometric Brownian motion models for assets and liabilities: from pension funding to optimal dividends. North American Actuarial Journal 7(3), 37-51]. 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 Hamilton-Jacobi-Bellman (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; Free; boundary; problem (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:33:y:2009:i:3:p:710-724

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