The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models

Abstract

Abstract:In this paper, several portfolio choice models are studied: a purely possibilistic model in which the return of the risky is a fuzzy number, and four models in which the background risk appears in addition to the investment risk. In these four models, risk is a bidimensional vector whose components are random variables or fuzzy numbers. Approximate formulas of the optimal allocation are obtained for all models, expressed in terms of some probabilistic or possibilistic moments, depending on the indicators of the investor preferences (risk aversion, prudence).

A Portfolio Choice Problem in the Framework of Expected Utility Operators

“…In the following subsection, we will recall the definition of the expected utility operators and a few generalities on them ( [18], [19]). We will introduce the D-operators by a property regulating the behaviour of an expected utility operator towards the derivation of the utility function with respect to a parameter.…”

“…Let us recall the expected utility operator. Definition 2.1 [18], [19] An (f -weighted) expected utility operator is a function T : F × C(R) → R such that for any a, b ∈ R, g, h ∈ C(R) and A ∈ F the following conditions are fulfilled:…”

“…In real life, on can consider risky asset as a fuzzy number. In paper [19], a possibilistic porfolio problem was formulated using the notion of possibilistic expected utility from [16] based in the framework of Zadeh' s possibility theory [32]. We determined an approximate calculation formula of the optimal solution in terms of the first three posibilistic moments of the fuzzy numbers representing the return of the risky asset and the investor's risk aversion and prudence indicators.…”

“…These two types of possibilistic variance have been studied in several papers (see e.g [4],[5],[13],[18],[34][5],[6],[7],[19],[25],[24],[30],[31]). …”

A Game-Theoretic Loss Allocation Approach in Power Distribution Systems with High Penetration of Distributed Generations

“…The suggested approach offers a criterion to which the result of different loss allocation techniques can be compared. In the concept of resources allocation, various frameworks are proposed to find an optimal allocation among agents [20,21]. Embedded cost allocation in cooperative games based on Shapley Value method provides stable decisions [22], where the resultant allocations are deemed to be the most equitable solution possible [23].…”