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. 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.
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- Alan L. Lewis, 1998. "Applications of Eigenfunction Expansions in Continuous-Time Finance," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 349-383.
- Leland, Hayne E, 1994.
" Corporate Debt Value, Bond Covenants, and Optimal Capital Structure,"
Journal of Finance,
American Finance Association, vol. 49(4), pages 1213-1252, September.
- Hayne E. Leland., 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Research Program in Finance Working Papers RPF-233, University of California at Berkeley.
- Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
- Vadim Linetsky, 2004. "Lookback options and diffusion hitting times: A spectral expansion approach," Finance and Stochastics, Springer, vol. 8(3), pages 373-398, 08.
- repec:spr:compst:v:51:y:2000:i:1:p:1-42 is not listed on IDEAS
- Rudolf, Markus & Ziemba, William T., 2004. "Intertemporal surplus management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 975-990, February.
- Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
- Hoevenaars, Roy P.M.M. & Molenaar, Roderick D.J. & Schotman, Peter C. & Steenkamp, Tom B.M., 2008. "Strategic asset allocation with liabilities: Beyond stocks and bonds," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2939-2970, September.
- Bjarne Hø jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182.
- Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327. Full references (including those not matched with items on IDEAS)
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