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Time stochastic s-convexity of claim processes

โœ Scribed by Michel Denuit

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
92 KB
Volume
26
Category
Article
ISSN
0167-6687

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โœฆ Synopsis

The purpose of this paper is to study the conditions on a stochastic process under which the s-convex ordering and the s-increasing convex stochastic ordering between two random instants is transformed into a stochastic ordering of the same type between the states occupied by this process at these moments. In this respect, the present work develops a previous study by Shaked and Wong (1995) [Probability in the Engineering and Informational Sciences 9, 563-580]. As an illustration, we show that the binomial and the Poisson processes, commonly used in actuarial sciences to model the occurrence of insured claims, possess this remarkable property.

๐Ÿ“œ SIMILAR VOLUMES

Weak convergence of convex stochastic pr
Weak convergence of convex stochastic processes
โœ Miguel A. Arcones ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 530 KB

We discuss the weak convergence of convex stochastic processes. Let {Z.(t): t e T }, n >/ 1, be a sequence of stochastic processes, where T is an open convex set of R e, such that Z, : T ~ R is a convex function (for each ~o and each n), We show that {Z,(t):ts To} converges weakly to {Z(t):t ~ T}, f