Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching jump-diffusion formulation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Jin, Zhuo¹  Wang, Yumin²  Yin, G.¹ 

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

关键词: Quantile hedging;    Variable annuities;    GMDBs;    Regime switching;    Markov chain approximation;   

DOI  :  10.1016/j.cam.2010.12.003

来源: Elsevier

【 摘 要 】

This work develops numerical approximation methods for quantile hedging involving mortality components for contingent claims in incomplete markets, in which guaranteed minimum death benefits (GMDBs) could not be perfectly hedged. A regime-switching jump-diffusion model is used to delineate the dynamic system and the hedging function for GMDBs, where the switching is represented by a continuous-time Markov chain. Using Markov chain approximation techniques, a discrete-time controlled Markov chain with two component is constructed. Under simple conditions, the convergence of the approximation to the value function is established. Examples of quantile hedging model for guaranteed minimum death benefits under linear jumps and general jumps are also presented. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free