Research Of Robust Utility Optimization Problem In Random Interval Income Markets

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 affected by incomplete information, investors’ subjective consciousness and so on. This paper studies the excepted utility maximization, stability of no-arbitrage property and utility maximization under model uncertainty when the underlying probability measure is uncertain.In a random interval income market, based on the robust no-arbitrage pricing principle, this paper obtains the risk neutral probability measure similar to classical random financial market. The price of contingent claim can be determined by future income and the risk neutral probability measure. The uncertainty of underlying probabilities induces the discussion of stability of robust no-arbitrage. This paper provides the condition to ensure the stability of robust no-arbitrage in view of total variation distance.This paper works on the utility maximization problem together with consumption and endowment based on weighted expected utility model. The paper discusses the utility maximization problem where utility function is influenced by uncertain future random state and random interval value, provides the condition to ensure the existence of optimal portfolio. Under the optimal expected utility portfolio background, the paper constructs the risk neutral probability measure, and offers the basic property of optimal weighted expected utility.Finally, this paper studies the utility maximization problem in which case the distribution of contingent payoff is uncertain. The information that can be obtained is only the one and second moment of underlying securities’ future payoffs, on the basis of the partial information, this paper constructs the robust weighted utility maximization model, formulating the original problem as bi-criterion objective, which can be reduced to solving a parametric quadratic problem.