The s-convex orders among real random variables, with applications

Abstract

Abstract. In this paper, new classes of stochastic order relations are introduced. These can be seen as extensions of the usual convex order and are closely related to the orderings discussed in Lefèvre and Utev (1996), as well as to the stochastic dominances in economics and stop-loss orders in actuarial sciences. These classes are studied in detail, including properties, characterizations, sufficient conditions, and extrema with respect to these orderings in different sets of distribution functions. Some applications illustrate the theory.Mathematics subject classification (1991): 60E15.

Stationary-excess operator and convex stochastic orders

“…We first obtain the s = 1, 2, 3-convex extrema when t = 1 (nonincreasing distributions). These were found earlier by Denuit et al (1999b) in the discrete case and Denuit et al (1998) in the continuous case. The method of proof used there, however, is quite different as it relies on a Khinchine representation for unimodal distributions.…”

“…More traditional illustrations in ruin theory and life insurance (as in Denuit and Lefèvre (1997) and Denuit et al (1998Denuit et al ( ), (1999b) could be considered too.…”

“…( ), (1999c, among others. The case, more traditional, of real-valued random variables was investigated by Rolski (1976), Levy (1992), Denuit et al (1998Denuit et al ( ), (1999b and in many other works.…”

Correlated risks, bivariate utility and optimal choices

“…For more details, we refer the interested readers to Denuit, Lefèvre & Shaked (1998) and Denuit, De Vijlder & Lefèvre (1999).…”

Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

“…The method of [16] is based on s-orderings (rather than on duality); for more on that method, see, e.g. [5]; concerning stochastic orders in general, see [25].…”