On The Randomized Schmitter Problem

Hansjörg Albrecher () and José Carlos Araujo-Acuna ()
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Hansjörg Albrecher: University of Lausanne, Switzerland and Swiss Finance Institute
José Carlos Araujo-Acuna: University of Bern

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 2, 515-535

Abstract: Abstract We revisit the classical Schmitter problem in ruin theory and consider it for randomly chosen initial surplus level U. We show that the computational simplification that is obtained for exponentially distributed U allows to connect the problem to m-convex ordering, from which simple and sharp analytical bounds for the ruin probability are obtained, both for the original (but randomized) problem and for extensions involving higher moments. In addition, we show that the solution to the classical problem with deterministic initial surplus level can conveniently be approximated via Erlang(k)-distributed U for sufficiently large k, utilizing the computational advantages of the advocated randomization approach.

Keywords: Schmitter problem; Ruin theory; Ruin probability; Laplace transform; Stochastic ordering; Erlangization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09910-5

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