基于BSSDEs的一般跳过程的可违约期权的定价模型

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.

Pricing a defaultable claim based on BSSDEs for general jump process

In this paper, we made a thorough study of pricing for defaultable claim with general jumps process by means of the mean-variance hedging method. We proposed a defaultable process representation theorem based on semimartingale process. Then we defined the variance-optimal martingale measure and constructed two backward stochastic semimartingale differential equations (BSSDEs) about control process and defaultable claim. Finally we derived the optimal investment strategy of minimizing the cost function, and gave the pricing formula of the defaultable claim with general jump process. The main contribution of this paper is that the BSSDE for the defaultable semimartingale process is given and the pricing formula for the defaultale claim is derived first time, it has some theoretical significance.