On The Randomized Schmitter Problem

Albrecher, Hansjörg; Araujo-Acuna, José Carlos (2021). On The Randomized Schmitter Problem (In Press). Methodology and computing in applied probability Springer 10.1007/s11009-021-09910-5

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Araujo-Acuna, José Carlos

Subjects:

500 Science > 510 Mathematics

ISSN:

1387-5841

Publisher:

Springer

Language:

English

Submitter:

José Carlos Araujo Acuna

Date Deposited:

01 Dec 2021 15:23

Last Modified:

01 Dec 2021 15:31

Publisher DOI:

10.1007/s11009-021-09910-5

BORIS DOI:

10.48350/161412

URI:

https://boris.unibe.ch/id/eprint/161412

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