Albrecher, Hansjoerg and Constantinescu, Corina and Palmowski, Zbigniew and Regensburger, Georg and 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 .
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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.
|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:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||M.G. Rosenkranz|
|Date Deposited:||30 Aug 2012 11:14|
|Last Modified:||01 Feb 2013 10:35|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/30376 (The current URI for this page, for reference purposes)|
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