适于风险厌恶型投资的美式看涨期权定价分析

An American Call Option Pricing Model for Risk-Averse Invertors

介绍了为风险厌恶型投资者所设计的新型美式看涨期权的数学模型.它的定价问题是一个退化的抛物型变分不等式,也是一个自由边界(即最佳实施边界)问题.与标准美式看涨期权不同,这种新型期权在股票分红时有两条光滑单调的自由边界,而当股票不分红时仅有一条直线型的自由边界.本文运用偏微分方程方法分析讨论解的存在唯一性,自由边界的单调性、连续性、可微性以及关于事先承诺的价格l的相关性质.

There is a new American call option which is designed for risk-averse invertors. The mathematical pricing model of this option can be formulated as a one-dimensional parabolie variational inequality, or equivalently, a free boundary problem. Different from the standard American call, it has two monotonous smooth free boundaries with dividends and has only one linear free boundary without dividends. To solve this problem, PDE arguments are applied. We can prove the existence and uniqueness of the solution. Then the properties of the free boundaries, such as monotonieity, smoothness, and location, are presented.