带跳的美式与永久美式期权的定价与停时

The Pricing of the Preferred Hedging Aermicancontingent Claims Under Transaction Costs

首先考虑报酬效用函数U(x)特殊情况下,运用最优停止理论,给出标的资产价格服从跳过程模型下美式期权的最优停时表达式,得到美式期权的最佳实施期为到期日T,此时美式期权变成欧式期权,并且期权的初始价值为C0*;其次,利用鞅方法讨论标的资产价格服从跳过程永久美式未定权益h(X1),得到最佳实施期为τ*,期权的初始价值为C*。

Considering return utility function U（x） under specific conditions, and using optimal stopping theories, we obtain optimal stopping formulas of American option based on the assumption that the process of underlying asset＇s pricing follows jump process, and make sure that American option＇s best tread time is the expiration date T. At the same time, American options becomes European options, and optionsinitial value is C0^＊ Next, by using the method of martingales, we discuss the optimal stopping formulas of perpetual American contingent claims h （ X1 ） and obtain its best tread time τ^＊ and its initial value C^＊ , bsed on the assumption that the process of underlying asset＇s pricing follows jump.