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

DOI10.1134/S0965542512100077zbMath1274.65334MaRDI QIDQ2838933

T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin

Publication date: 3 July 2013

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

algorithmnumerical examplessingular boundary value problemfinancial marketCramer-Lundberg modelweak singularitysecond-order linear integro-differential equationdynamic insurance model

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20)

Related Items (11)

In the insurance business risky investments are dangerous: the case of negative risk sums ⋮ INVESTIGATION OF SOME CLASSES OF SECOND ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH A POWERLOGARITHMIC SINGULARITY IN THE KERNEL ⋮ Dynamical insurance models with investment: constrained singular problems for integrodifferential equations ⋮ On the improved thinning risk model under a periodic dividend barrier strategy ⋮ Viscosity Solutions of Integro-Differential Equations for Nonruin Probabilities ⋮ Singular initial-value and boundary-value problems for integrodifferential equations in dynamical insurance models with investments ⋮ Ruin probabilities with investments: smoothness, inegro-differential and ordinary differential equations, asymptotic behavior ⋮ New type super singular integro-differential equation and its conjugate equation ⋮ Mellin transform and integro-differential equations with logarithmic singularity in the kernel ⋮ Ruin probability in models with stochastic premiums ⋮ Solvency of an insurance company in a dual risk model with investment: analysis and numerical study of singular boundary value problems

Cites Work

• Aspects of risk theory
• Power tailed ruin probabilities in the presence of risky investments.
• In the insurance business risky investments are dangerous
• Singular cauchy problems for systems of ordinary differential equations
• Evaluation of the eigenvalues and eigenfunctions of ordinary differential equations with singularities
• Singular Problems for Integro-differential Equations in Dynamic Insurance Models
• On the transfer of boundary conditions for systems of ordinary linear differential equations (a variant of the dispersive method)
• On the transfer of the condition of boundedness for some systems of ordinary linear differential equations
• Discovery of the solutions of certain systems of differential equations with a given condition at infinity. I
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