Stochastic Modeling

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By Aoki M.

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To be more specific in the above example, A does not dominate E. However, if we also had: EA U ( X ) > EE U ( X ) for all U G U, it would not add anything to the partial ordering because investment E is already dominated by investment B and hence it is inefficient and no investor will select it. The partition of the feasible set, FS, to the efficient set (ES) and inefficient set (IS) depends on the information available. In the above example, we assume the information, U G Ui. If, for example, in addition to U ' > 0, we assume also that U " < 0 or any other relevant information, we will get another partition of the FS to IS and ES reflecting this additional information.

Moreover, in this framework, there is no need to define risk. This chapter deals with the foundations of expected utility theory. We will first discuss a number of investment criteria and then we will analyze how these decision criteria are related to the expected utility framework. 2 INVESTMENT CRITERIA a) The Maximum Return Criterion (MRC). The Maximum Return Criterion (MRC) is employed when there is no risk at all. According to this rule, we simply choose the investment with the highest rate of return.

Generally speaking, for any given piece of information, the smaller the efficient set relative to the feasible set, the better off the investors. To demonstrate this, suppose that there are 100 mutual funds (investments) and an investment consultant wishes to advise his clients which funds to buy. Assume that the only information known is that U G Ui. Suppose that the consultant has an investment decision rule corresponding to this information. Employing this rule, the FS is divided into the ES and the IS.

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