Portfolio-consumption Problem With Options

With the continuous improvement and development of the financial market , many financial derivative products, such as options, future contracts, etc, will gradually become the main transaction object of the financial market. Therefore, when investors' investment objects contain options, how to arrange their own in-vestment and consumption is the actual problem that the current investors face. On the basis of the Morton investment-consumption model, the paper discusses the investors' optimal portfolio-consumption problem on the assumption that in-vestors'investment objects contain a european-style call option. We build utility maximization model, and by using stochastic dynamic programming principles we get the optimal portfolio-consumption strategy about exponential utility func-tion,Then we get the corresponding hedging strategy, and compare it with the investment strategy, finally we obtain the conclusion that the optimal portfolio-consumption strategy is better than the the corresponding hedging strategy.