Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching jump-diffusion formulation
type: Item
instance of: scholarly article
title: Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching jump-diffusion formulation
zbMATH Open document ID: 1229.91358
author: Zhuo Jin
author: Yu-Min Wang
author: G. Yin
published in: Journal of Computational and Applied Mathematics
publication date: 2011-03-09T00:00:00Z
review text: This paper considers hedging problems containing both financial and insurance risk and perfect hedging is impossible because of the mortality risk, and the incompleteness of the market, due to regime switching. In the proposed model, the rate of return and the volatility, and the insurance charge, are modulated by a finite-state Markov chain, which represents the market modes and other economic conditions. To find the optimal hedging strategies, it is needed to solve a system of Hamilton-Jacobi-Bellman (HJB) integro-differential equations. Using Markov chain approximation techniques, a discrete-time controlled Markov chain with two components is constructed. Under simple conditions, the convergence of the approximation to the value function is established. Examples of quantile hedging for guaranteed minimum death benefits are also presented..
Mathematics Subject Classification ID: 91G70
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 5863181
zbMATH Keywords: quantile hedging
zbMATH Keywords: variable annuities
zbMATH Keywords: GMDBs
zbMATH Keywords: regime switching
zbMATH Keywords: Markov chain approximation
reviewed by: Pedro A. Morettin
MaRDI profile type: Publication
full work available at URL: j.cam.2010.12.003
OpenAlex ID: W2052985179
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DOI: 10.1016/J.CAM.2010.12.003
description: scientific article; zbMATH DE number 5863181