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Integral equations and actuarial risk management: Some models and numerics

    A. Makroglou Affiliation

Abstract

The problem of the estimation of the probability R(z, t) (here t is time, z is initial reserve) of the finite time non‐ruin problem for a risk business such as an insurance company is considered, with respect to



  • presenting models that have been used in the literature in the form of integral / integro‐differential equations,

  • reviewing some analytical and computational methods used for their solution,

  • presenting numerical results obtained with one method (a global Lagrange type approximation in the z—space).


Integralinės lygtys ir aktuarijų rizikos vadyba: kai kurie modeliai ir skaičiavimai


Santrauka


Sprendžiamas tikimybes R(z,t) (t‐laikas, z‐pradiniai rezervai) ivertinimo uždavinys, kur R(z,t)tikimybe, kad verslo (tarkime, draudimo) bendrove nesubankrutuos per baigtini laika t. Tuo tikslu naudojami literatūroje aprašyti integraliniai ir integrodiferencialiniai modeliai, apžvelgiami kai kurie analiziniai ir skaitiniai lygčiu sprendimo metodai, pateikiami skaičiavimu, gautu vieno metodo globalines Lagranžo tipo aproksimacijos z‐erdveje pagalba, rezultatai.


First Published Online: 14 Oct 2010

Keyword : Partial Volterra integro‐differential equations, first order, numerical solution, global Lagrange type approximations, actuarial risk management, finite time collective non‐ruin

How to Cite
Makroglou, A. (2003). Integral equations and actuarial risk management: Some models and numerics. Mathematical Modelling and Analysis, 8(2), 143-154. https://doi.org/10.3846/13926292.2003.9637219
Published in Issue
Jun 30, 2003
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