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Spectral decomposition of optimal asset-liability management

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  • Decamps, Marc
  • De Schepper, Ann
  • Goovaerts, Marc

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.

Suggested Citation

  • Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2009. "Spectral decomposition of optimal asset-liability management," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 710-724, March.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:3:p:710-724
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    References listed on IDEAS

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    Cited by:

    1. Benjamin Avanzi & Ping Chen & Lars Frederik Brandt Henriksen & Bernard Wong, 2022. "On the surplus management of funds with assets and liabilities in presence of solvency requirements," Papers 2203.05139, arXiv.org, revised Aug 2022.
    2. Lucian Gaban & Ionut - Marius Rus & Alin Fetita & Liviu Bechis, 2017. "Assets And Liabilities Management During The Crisis - A Study On Banks In Romania," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 529-537, July.
    3. Benjamin Avanzi & Vincent Tu & Bernard Wong, 2016. "A Note on Realistic Dividends in Actuarial Surplus Models," Risks, MDPI, vol. 4(4), pages 1-9, October.

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