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.