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本文研究不完备市场情况下的可违约期权的动态指数效用无差异定价.不同于大多数的可违约期权定价文献,本文没有假定鞅的不变性,即通常的H假设,而是通过信息流的扩张和测度的变换,将信用风险敏感的资产转换为一个G局部鞅,其后引入一个具体的倒向随机微分方程(BSDE),并证明该方程解的存在性与唯一性;然后利用无差异价值过程C t(B,α)在最小熵鞅测度下对一般的投资策略为上鞅,而在最优投资策略下为鞅的事实,证明无差异价值过程C t(B,α)就是BSDE的解,从而给出可违约期权的定价.
In this paper, we study the non-difference pricing of the dynamic exponential utility of defaultable options in the case of an incomplete market. Unlike most of the literature on defaultable option pricing, this paper does not assume the invariance of martingale, ie the usual H-hypothesis, Expansion and measure transformation, the credit risk-sensitive assets are transformed into a G-local martingale, then a specific backward stochastic differential equation (BSDE) is introduced, and the existence and uniqueness of the solution of the equation are proved. Then, The value process C t (B, α) is a martingale for the general investment strategy under the minimum entropy martingale measure and martingale under the optimal investment strategy. It is proved that the indifference value process C t (B, α) is BSDE Of the solution, giving the price of defaulting options.