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...

This paper established the ARMA-GJR-AL model of dynamic risk VaR and CVaR measurement. Considering from aspects of the correlation and volatility and residual distribution characteristics, studying the dynamic risk measures of VaR and CVaR based on ARMA-GJR-AL model. Through empirical research, Risk prediction and accuracy of inspection are given of the Shanghai stock market and the New York st...

We propose a new estimator for expected shortfall that uses asymptotic expansions to account for the asymmetry and heavy tails in financial returns. We provide all the necessary formulas for decomposing estimators of value-at-risk and expected shortfall based on asymptotic expansions and show that this new methodology is very useful for analyzing and predicting the risk properties of portfolios...

This paper presents analytical solutions to the problem of how to calculate sensible VaR (Value-at-Risk) and ES (Expected Shortfall) contributions in the CreditRisk+ methodology. Via the ES contributions, ES itself can be exactly computed in finitely many steps. The methods are illustrated by numerical examples.

Independent risks are substitutes if the opportunity to invest in one risk cuts down the demand in the others. Intuition seems to sustain this idea, but if the problem is tackled in a normative framework, no consensus in the literature is found. In this paper we investigate what does happen if the decision rule is based on the Generalized Sharpe Ratio. The answer depends on the risk measure und...

This paper employs uncertain programming to deal with optimal assignment problem with uncertain profits. Within the framework of uncertain programming, a concept of expected optimal assignment for uncertain optimal assignment problem is proposed, and then an expected value model is constructed. Taking advantage of properties of uncertainty theory, this model can be transformed into a correspond...

Piccione and Rubinstein argue that a seemingly paradoxical form of time inconsistency can arise in games of imperfect recall. Their argument depends on calculating the expected value of a game from the standpoint of a player in the middle of play. We claim that this concept is not well deened in games with ab-sentmindedness (where two nodes on a path can be in the same information set) without ...

Let P be a set of points in R, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a well-defined random distribution. We consider two distributions; in the first distribution (which we call the Bernoulli distribution), each point p ∈ P is included ...

A normally distributed fuzzy variable is defined by a unimodal and symmetric membership function, and is proved to be the most uncertain one when expected value and variance are given. In this note, a lognormally distributed fuzzy variable is defined and the membership function, expected value and variance of this variable are discussed. Based on these results, some properties about geometric L...

The value of a methodological paper generally depends on 1) the importance of the problem addressed, 2) the completeness of the presentation of the issues and prior progress, and 3) a new solution to the problem that is feasible and better than what has already been proposed. The Uyei and Braithwaite article (hereafter UB) clearly satisfies the first two criteria and is well worth contemplating...