应用数学学报  2013, Vol. 36 Issue (6): 1053-1071    DOI:
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Regime Switching Lėvy模型下的局部风险最小套期保值策略

1. 宁波大学数学系, 宁波 315211;
2. 华东师范大学金融与统计学院, 上海 200241;
3. 江西师范大学数学与信息科学学院, 南昌 330022
Locally Risk Minimizing Hedging Strategy Under a Regime Switching Lėvy Model
WANG Wei1, QIAN Linyi2, WEN Limin3
1. Department of Mathematics, Ning Bo University, Ningbo 315211;
2. School of Finance and Statistics, East China Normal University, Shanghai 200241;
3. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022
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Abstract： In this paper, we suppose that the risky asset follows a Markov-modulated Geometric Lėvy process, the market interest rate, the appreciation rate and the volatility rate of the risky asset, and the intensity and magnitude of the jump depend on the states of the economy which are described by a continuous-time Markov chain. Since the market which we considered is incomplete, we find an optimal hedging strategy for a European contingent claim by employing the local risk minimization method. Then we also provide an example and obtain the numerical result of an optimal risk hedging strategy for a European call option under a Markov-modulated Geometry Brownian motion. Finally, this optimal risk hedging strategy and the Delta hedging strategy under the Black-Scholes model are compared in this paper, and prove that the uncertain factors of Markov chain will bring the impact on the investment decision of risk manager.

 引用本文: 王伟,钱林义,温利民. Regime Switching Lėvy模型下的局部风险最小套期保值策略[J]. 应用数学学报, 2013, 36(6): 1053-1071. WANG Wei,QIAN Linyi,WEN Limin. Locally Risk Minimizing Hedging Strategy Under a Regime Switching Lėvy Model[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(6): 1053-1071.

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