An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts
AbstractThis paper develops an extended constant elasticity of variance (E-CEV) model to overcome the shortcomings of the general CEV model. Under the E-CEV model, we study the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid by annuity. By applying the Legendre transform, dual theory and an asymptotic expansion approach, we respectively derive two asymptotic strategies for a CRRA and CARA utility functions in two different periods. Furthermore, we find that each asymptotic strategy can be decomposed into an optimal zero-order strategy and a perturbation strategy. The optimal zero-order strategy denotes an investment strategy where the current volatility is just equal to the mean level of the volatility, whereas the perturbation strategy provides an approximation solution to hedge the slow varying nature of the current volatility deviating from mean level. Finally, we find that the optimal zero-order strategy under given conditions will reduce to the results of Devolder etÂ al. (2003), Xiao etÂ al. (2007) and Gao (2009), respectively.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 46 (2010)
Issue (Month): 3 (June)
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Web page: http://www.elsevier.com/locate/inca/505554
Defined contribution pension plan Stochastic optimal control Legendre transform CEV model Asymptotic expansion;
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