On Risk Measure With Random Interval Payoffs

In recent years, people attended that the actual investment often covered a subjective element and incompletion random information, which can not be modeled by stochastic models. For financial theories need to act in more general uncertain market, this thesis describes the risk measure with random interval payoffs, introduces the relationship between the risk measure with random interval payoffs and the risk measure with random variable payoffs, the relationship between the optimized certainty equivalent and risk measure and mean-risk model.Risk measure with random interval returns is studied by risk measure with random variable returns. Based on random interval definition and calculation relations and coherent risk measure for random assets, two same concepts are extended toward assets with random interval payoffs. And we definite the acceptance set, and analyse the relationship between risk measure and the acceptance set.The relationship between the risk measure with random interval payoffs and the risk measure with random variable payoffs is studied. Based on the risk measure with random variable payoffs, we built three kinds of risk measure with random interval returns.Risk measure based on random interval is a new way to study. Combining the the relationship between the optimized certainty equivalent and risk measure with random variable payoffs, this relationship is studied with random interval. The mean-risk model is also studied, and the efficient frontier is introduced. A portfolio selection model with CVaR or another risk measure in random interval market is proposed and discussed, and an illustrative example is used to prove this thesis.Risk measure with random interval consider the uncertain factors, and it can solve the problem of asset allocation successful by changing the uncertain factors to cetain. It is better to adapt to reality market.