中文摘要：

研究了由马尔可夫交换Levy过程的随机指数所驱动的风险资产的期权定价问题,即市场的利率、风险资产的波动率以及N个状态的补偿子都依赖于不可观的经济状态,而这些经济状态服从于一个连续时间的隐马氏链模型.一般地,由马尔可夫交换Levy过程的随机指数所描述的市场是不完备的,因此,鞅测度不是唯一的.通过采用状态转换Esscher变换来确定等价鞅测度,并且证明了所得到的定价测度就是最小熵鞅测度.

英文摘要：

The option pricing problem when the underlying risky assets are driven by stochastic exponential of Markov switching Levy process is considered.That is,the market interest rate,the volatility of the underlying risky assets and the N-state compensator, depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.The market described by the stochastic exponential of Markov switching Levy process is incomplete in general.Hence,the martingale measure is not unique.The authors adopt a regime switching Esscher transform to determine an equivalent martingale pricing measure.The pricing result can be justified by the minimal entropy martingale measure（MEMM）.