| 一类带马氏切换与时滞的未定权益模型的对冲策略 |
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| 引用本文： | 张玢玢,胡良剑.一类带马氏切换与时滞的未定权益模型的对冲策略[J].南京气象学院学报,2016,8(6):518-523. |
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| 作者姓名： | 张玢玢 胡良剑 |
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| 作者单位： | 东华大学 理学院, 上海, 201620;东华大学 理学院, 上海, 201620 |
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| 基金项目： | 国家自然科学基金（11471071）；上海市自然科学基金（14ZR1401200） |
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| 摘 要： | 在风险资产服从一类带马尔科夫模式切换（马氏切换）的时滞随机微分方程模型的情形下，考虑了一个以上述风险资产为标的资产的欧式未定权益，利用Esscher变换找到了等价鞅测度，并在此基础上得到该权益价格过程的鞅表示.同时，在资产价格过程的系数满足一定条件的假设下，给出了在由马氏切换的出现而导致的不完备市场中，通过最小化残余风险而求得的最优连续对冲策略.
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| 关 键 词： | 对冲 马尔科夫模式切换(马氏切换) 时滞 随机微分方程 |
| 收稿时间： | 2016/5/16 0:00:00 |
Hedging strategy for a class of contingent claim model with delay and Markov switching |
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| ZHANG Binbin and HU Liangjian.Hedging strategy for a class of contingent claim model with delay and Markov switching[J].Journal of Nanjing Institute of Meteorology,2016,8(6):518-523. |
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| Authors: | ZHANG Binbin and HU Liangjian |
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| Institution: | Depatment of Applied Mathematics, Donghua University, Shanghai 201620;Depatment of Applied Mathematics, Donghua University, Shanghai 201620 |
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| Abstract: | This paper considers the hedging problem for a class of stochastic differential delay equations with Markov switching.When the price process of a risky asset follows the considered model,we derive a martingale representation for the price process of a contingent claim written on the risky asset with respect to an equivalent martingale measure obtained by the Esscher transform.Then,under some conditions for the coefficients of the model,we identify the continuous-time hedging strategy by minimizing the residual risk in the incomplete market due to the additional source of uncertainty introduced by the regime switching. |
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| Keywords: | hedging Markov switching delay stochastic differential equations |
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