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本文采用均值-方差对冲方法,对具有一般跳过程,存在违约风险的期权定价做了深入研究.首先建立了基于违约过程的半鞅的鞅表示定理,其次定义最优方差鞅测度并构建两个倒向半鞅随机微分方程,然后找出使成本函数最小的最优投资策略,从而给出其定价公式.本文的主要贡献在于首次给出了可违约半鞅过程的倒向随机半鞅微分方程,并且给出了具有一般跳过程的可违约期权的定价公式,具有一定的理论意义.
In this paper, the method of mean-variance hedging is used to study the pricing of options with general jump process and default risk.Firstly, the martingale representation theorem of semi-martingale is established based on the default process, the optimal variance martingale measure is defined and two Backward to the semi-martingale stochastic differential equations, and then find the optimal investment strategy that minimizes the cost function, and then give its pricing formula.The main contribution of this paper is the first time to give the backward stochastic semi-martingale differential equation , And gives the pricing formula of defaulting options with a general jump process, which has some theoretical significance.