Stochastic Dominance: Investment Decision Making under by Haim Levy

By Haim Levy

This booklet is dedicated to funding decision-making less than uncertainty. The publication covers 3 easy methods to this procedure: the stochastic dominance method; the mean-variance process; and the non-expected software process, targeting prospect idea and its converted model, cumulative prospect idea. every one process is mentioned and in comparison. additionally, this quantity examines situations within which stochastic dominance ideas coincide with the mean-variance rule and considers how contradictions among those methods may perhaps ensue.

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Additional resources for Stochastic Dominance: Investment Decision Making under Uncertainty (Studies in Risk and Uncertainty)

Sample text

First , note that by the comparability axiom, we are able to compare the Ai. Moreover, because of the monotonicity axiom we can determine that: Ai < A2 < An implies Aj -< A2 ^ .... An. EXPECTED UTILITY THEORY 35 Define A* = { ( 1 - U(Ai)) A , U(Ai) An } where 0 < U (A) < 1. By the continuity axiom, for every A , there is a probability U(Ai) such that: Note that for Ai, we have U(Ai) - 0; hence A] ~ Ai and for An ,U(An) = 1, hence An ~ An. PiA* axiom, we obtain: p„A„} where the superscript of Li indicates that one element Aj has been substituted in L.

One investor might decide on U(A2) - Ml. Another investor who dislikes uncertainty might decide on U(A2) - 3/4. Because U(A2) varies from one investor to another according to his/her taste or preference, it is called the utility function, or the utility assigned to the value A2. Therefore, U(Ai) is called the utility of Ai , and the investment with the highest expected utility Z Pi U(Ai) is the optimal investment. The function U(Ai) has only one property: It is U(Ai) = 0 for the lowest value Ai and U(An) = 1 for the highest value (see Footnote 6) An and, due to the monotonicity axiom, it increases (in the weak sense) as Ai increases.

This rule, called First Degree Stochastic Dominance (FSD), is appropriate for all investors with U' > 0 (with a strict inequality at some range). Let us use this decision rule (any other rule corresponding to other partial information can be used in a similar way) to introduce some definitions, all of which are commonly used in the financial literature and which are needed for the explanation of partial and complete ordering. The feasible set (FS) is defined as the set of all available investments under consideration.

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