Exact and asymptotic results for insurance risk models with surplus-dependent premiums

Albrecher, Hansjoerg, Constantinescu, Corina, Palmowski, Zbigniew, Regensburger, Georg, Rosenkranz, Markus (2013) Exact and asymptotic results for insurance risk models with surplus-dependent premiums. SIAM Journal on Applied Mathematics, 73 (1). pp. 47-66. ISSN 0036-1399. (doi:10.1137/110852000) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:30376)

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Official URL: http://dx.doi.org/10.1137/110852000

Abstract

In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cram\'er-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.

Item Type:	Article
DOI/Identification number:	10.1137/110852000
Uncontrolled keywords:	Renewal risk models; surplus dependent premiums; boundary value problems; Green's operators; asymptotic expansions.
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Markus Rosenkranz
Date Deposited:	30 Aug 2012 11:14 UTC
Last Modified:	16 Feb 2021 12:41 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/30376 (The current URI for this page, for reference purposes)

University of Kent Author Information

Rosenkranz, Markus.

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