含期权的最优投资消费决策

当投资对象中含有期权时如何安排自己的投资和消费是当前投资者所面临的实际问题。本文在Black-Scholes模型假设的市场条件下,假定投资者的投资对象中含有一个欧式看涨期权,讨论了在该情形下投资者如何进行投资和消费的问题。建立效用最大化模型,应用最优控制原理得到了关于指数效用函数的最优投资消费策略,另外还得到了投资者的套期保值策略,并对这两种策略进行了对比,得到了它们之间的关系式。最后给出了数值示例验证了最优策略优于套期保值策略。

Optimal Investment and Consumption Decisions Including Option

When option is included in investment objects,how to arrange his(her)investment and consumption proportions is becoming a practical problem faced by all current investors.Under the market conditions supposed in Black-Scholes model and assumption that an investment object is a European call option,in this paper an investment-consumption problem is investigated.A utility maximization model is constructed.By applying the optimal control principle,the optimal investment consumption strategies for the exponential utility function are derived.In addition,the hedging strategies are also presented.The hedging strategies is compared with the optimal strategies,and their relation equation is obtained.Finally,a numerical example is given to verify that the optimal strategies are better than the hedging strategies.