Spectral decomposition of optimal asset-liability management
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Katholieke Universiteit Leuven in its series Open Access publications from Katholieke Universiteit Leuven with number urn:hdl:123456789/202162.
Date of creation: Mar 2009
Date of revision:
Publication status: Published in Journal of economic dynamics & control (2009-03) v.33, p.710-724
Contact details of provider:
Web page: http://www.kuleuven.be
Other versions of this item:
- 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.
- NEP-ALL-2010-02-13 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alan L. Lewis, 1998. "Applications of Eigenfunction Expansions in Continuous-Time Finance," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 349-383.
- 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.
- 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 351-67, May.
- 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.
- 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," Open Access publications from Maastricht University urn:nbn:nl:ui:27-23093, Maastricht University.
- 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 H�jgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor and Francis Journals, vol. 4(3), pages 315-327.
- Leland, Hayne E, 1994.
" Corporate Debt Value, Bond Covenants, and Optimal Capital Structure,"
Journal of Finance,
American Finance Association, vol. 49(4), pages 1213-52, 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.
- Vadim Linetsky, 2004. "Lookback options and diffusion hitting times: A spectral expansion approach," Finance and Stochastics, Springer, vol. 8(3), pages 373-398, 08.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carl Demeyere).
If references are entirely missing, you can add them using this form.