This note shows how Yaari (1987)'s dual theory of choice under risk naturally extends to the case of incomplete preferences. This also provides an axiomatic characterization of a large and widely studied class of stochastic orders used to rank the riskiness of random variables or the dispersion...

Topp-Leone distribution is a continuous unimodal distribution with bounded support (recently rediscovered) which is useful for modelling life-time phenomena. In this paper we study some reliability measures of this distribution such as the hazard rate, mean residual life, reversed hazard rate,...

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level...

We investigate whether several families of generalized quantiles (expectiles, Lp-quantiles and M-quantiles) respect various stochastic orders (the usual stochastic order, the convexity order, and the p-convexity orders).

Using a standard reduction argument based on conditional expectations, this paper argues that risk sharing is always beneficial (with respect to convex order or second degree stochastic dominance) provided the risk-averse agents share the total losses appropriately (whatever the distribution of...

Orderings of interdependence are useful in many economic contexts: in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore five orderings of interdependence for...

This paper studies capital allocation problems using a general loss function. Stochastic comparisons are conducted for general loss functions in several scenarios: independent and identically distributed risks; independent but non-identically distributed risks; comonotonic risks. Applications in...

A general method of introducing a parameter, called tilt parameter, has been discussed by Marshall and Olkin (1997) to give more flexibility in modelling. In this paper, we take the tilt parameter of the Marshall–Olkin extended family as a random variable. The closure of this model under...

Orderings of interdependence among random variables are useful in many economic contexts, for example, in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore...