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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 33 (2009)
Issue (Month): 3 (March)
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Web page: http://www.elsevier.com/locate/jedc
Asset-liability management HJB principle Local time Spectral theory Free boundary problem;
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