Research Of Utility Optimization Problem In Random Interval Income Markets And Its Application

In a random interval income market, the profits and losses of risk assets can be expressed in random interval, which can reflect the asset value that can be affected by incomplete information, investors’subjective consciousness and so on. The expected utility analysis under the traditional stochastic financial model is extended to the random interval model of financial markets. On the basis of expected utility optimization models, pricing problem of random interval valued assets are also studied.Firstly, on the basis of the evaluation of interval numbers, combining with the definition of the random interval expectation, introducing the pessimism coefficient which can reflects investors’attitude to interval uncertain models, this paper put forward a weighted expected utility model to measure the expected utility of random interval valued assets. We also studied the definite equivalence concept of random interval valued assets, and based on the weighted expected utility maximization, analysed the investment portfolio of single random interval value assets and risk-free assets.Secondly, we discussed the existence problem of optimal portfolio about multiple random interval value financial assets. We first prove that the existence of optimal portfolio under the assumption of two kinds of utility function. In the market without robust arbitrage portfolio, the optimal investment portfolio exists. And we got a risk neutral probability measure in the random interval market without robust arbitrage through the optimal portfolio.Thirdly, using the weighted expected utility maximization, this paper discussed the fair pricing and indifference pricing of random interval contingent claim. On the basis of fair pricing in the traditional random financial market, the paper put forward the fair pricing concept of random interval contingent claim, and got the fair price interval. The results show that, the endpoint of fair price interval is the robust no-arbitrage price of contingent claim. These conclusions are parallel to the corresponding ones in traditional random financial market. And when the random interval valued assets degenerates into random variables value assets, these conclusions are consistent with what is we got from traditional random financial market.In the analysis of the indifference pricing of random interval contingent claim, firstly according to basic principles of indifference pricing in random market, the paper given the concept of random interval valued assets pricing. Secondly under the two forks tree background, taking the random interval income market model as an example, this paper studied the indifference pricing problem with exponential utility function, and gave an example to illustrate how to get the price.