Knight不确定下基于无穷纯跳Levy过程的一般风险资产的动态最小定价

摘要

研究了具有Knight不确定性的金融市场下的一般风险资产的动态最小定价，利用倒向随机微分方程（BSDE）理论以及时间－风险折现方法，推导出了基于无穷纯跳 Levy过程的一般风险资产在实际概率测度下的动态定价公式及其在Knight不确定性控制集合上的动态最小定价。最后给出了一个欧式看涨期权动态最小定价的例子，并导出期权价格的显示表达式。在 Knight不确定环境下，引入 Levy过程来描述股票价格的动态走势，更加符合实际市场，可广泛地应用于一般风险资产的定价过程，这为投资分析提供一定的理论依据。%By using the theories of backward stochastic differential equation and time-risk discount method,dynamic minimal pricing of general risk assets was studied under the financial market with Knight uncertainty.Dynamic pricing formula of general risk assets was deduced based on infinite pure j ump Levy process under real probability measure.Moreover,dynamic minimal pricing formula was calculated in a set of Knight uncertainty.Finally,a case of dynamic minimal pricing of European call option was presented and the explicit solutions of the price of the option was obtained.The Levy process was introduced to describe dynamic movements of stock prices under Knight uncertain environment,which was more in line with actual market and could be widely used in general risk assets pricing,because it provided the theoretical basis for investment analysis.