Optimality Conditions in Portfolio Analysis with Generalized Deviation Measures
نویسندگان
چکیده
Optimality conditions are derived for problems of minimizing a generalized measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. Generalized measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality conditions are applied to characterize the generalized “master funds” which elsewhere have been developed in extending classical portfolio theory beyond the case of standard deviation. The consequences are worked out for deviation based on conditional value-at-risk and its variants, in particular.
منابع مشابه
Optimality conditions in portfolio analysis with general deviation measures
Optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. General measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality con...
متن کاملOptimality conditions for portfolio optimization problems with convex deviation measures as objective functions
Abstract. In this paper we derive by means of the duality theory necessary and sufficient optimality conditions for convex optimization problems having as objective function the composition of a convex function and a linear continuous mapping defined on a separated locally convex space with values in an finitedimensional space. We use the general results for deriving optimality conditions for t...
متن کاملMaster funds in portfolio analysis with general deviation measures
Generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, derived for example from conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors. The...
متن کاملThe KKT optimality conditions for constrained programming problem with generalized convex fuzzy mappings
The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...
متن کاملPortfolio Analysis with General Deviation Measures
Generalized measures of deviation, as substitutes for standard deviation, are considered in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, associated for example with conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors...
متن کامل