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Orderings of risks: A comparative study via stop-loss transforms. (English) Zbl 0855.62095

Summary: The relations between the following concepts for ordering risks are investigated: stochastic dominance, stop-loss order, convex order and being more dangerous. Using characterizations via stop-loss transforms, we give an elementary proof of the separation theorem for stop-loss order, and we correct a mistake in a result of E. A. van Heerwaarden [Ordering of risks: Theory and actuarial applications. Tinbergen Inst. Ser. 20 (1991)] on the connection between stop-loss order and being more dangerous. This is done by introducing a new notion of convergence for distributions. Moreover, we consider lattice properties of these orders.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
62E10 Characterization and structure theory of statistical distributions
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