Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

Autor: N. B. Konyukhova, S. V. Kurochkin, T. A. Belkina
Rok vydání: 2012
Předmět:
Zdroj: Computational Mathematics and Mathematical Physics. 52:1384-1416
ISSN: 1555-6662
0965-5425
Popis: A singular boundary value problem for a secondorder linear integrodifferential equation with Volterra and nonVolterra integral operators is formulated and analyzed. The equation is defined on +, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lun� dberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deter� ministic premiums is given. DOI: 10.1134/S0965542512100077
Databáze: OpenAIRE
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