Integral equations and actuarial risk management: Some models and numerics

    A. Makroglou Info

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 tikimybės R(z, t) (t – laikas, z – pradiniai rezervai) įvertinimo uždavinys, kur R(z, t) –tikimybė, kad verslo (tarkime, draudimo) bendrovė nesubankrutuos per baigtinį laiką t. Tuo tikslu naudojami literatūroje aprašyti integraliniai ir integrodiferencialiniai modeliai, apžvelgiami kai kurie analiziniai ir skaitiniai lygčių sprendimo metodai, pateikiami skaičiavimų, gautų vieno metodo globalinės Lagranžo tipo aproksimacijos z – erdvėje pagalba, rezultatai.

First Published Online: 14 Oct 2010

Keywords:

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

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June 30, 2003
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2003-06-30

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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

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