We consider the probability of ruin of a pension fund on a finite time interval. The basis is provided by the standard Cramer–Lundberg model, which is modified by specifying enrolment and contribution parameters in the form of random variables. A number of factors may be treated as random variables in the model: the date of member’s death, members’ wages, the number of fund members, financial indicators (discounting and return rates, inflation, wage growth rates). Each of these factors specified as a random variable affects the nondeterministic behavior of the fund’s receipts and payouts. In this article, the random factors include the number of members joining the pension fund in the relevant year and random mortality.
Similar content being viewed by others
References
N. Bowers, H. Gerber, J. Hickman, D. Jones, and C. Nesbitt, Actuarial Mathematics [Russian translation], Yanus-K, Moscow (2001).
A. V. Boikov, “Cramer–Lundberg model with stochastic premiums,” Teoriya Veroyatnostei i Ee Primeneniya, 47, No. 3, 549–553 2002.
O. P. Vinogradov, “An elementary method for estimating ruin probabilities,” Obozrenie Prikladnoi i Promyshlennoi Matematiki, 5, No. 1, 134–149 (1998).
E. V. Glukhova, O. A. Zmeev, and K. I. Livshits, Mathematical Insurance Models [in Russian], Izd. Tomsk. Univ., Tomsk, Russia (2004).
V. Yu. Korolev, V. E. Bening, and S. Ya. Shorgin, Mathematical Foundations of Risk Theory [in Russian], Fizmatlit, Moscow (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 55, 2017, pp. 97–109.
Rights and permissions
About this article
Cite this article
Belolipetskii, A.A., Lepskaya, M.A. A Mathematical Model of Pension Fund Operation and Methods of Fund Stability Analysis. Comput Math Model 29, 233–243 (2018). https://doi.org/10.1007/s10598-018-9404-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-018-9404-7