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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 9, Pages 1473–1490
DOI: https://doi.org/10.31857/S0044466922090058 (Mi zvmmf11447) 		 
Optimal control

Optimal control of investment in a collective pension insurance model: study of singular nonlinear problems for integro-differential equations

T. A. Belkinaa, N. B. Konyukhovab, S. V. Kurochkinb

a Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466922090058
Abstract: For a collective pension insurance model (dual risk model), the optimal control of investments aimed at maximizing the survival probability of an insurance company is considered. The search for an optimal strategy by applying dynamic programming leads to singular nonlinear boundary value problems for integro-differential equations. In the case of an exponential premium size distribution, these problems are studied analytically. Numerical results are presented and compared with previous computations in the case of simple investment strategies (risky and risk-free) in the considered model.
Key words: collective pension insurance model, survival probability of an insurance company, optimal control of investments, Bellman equation, exponential premium size distribution, nonlinear integro-differential equations, singular boundary value problems.
Received: 03.03.2022
Revised: 26.03.2022
Accepted: 11.05.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 9, Pages 1438–1454
DOI: https://doi.org/10.1134/S0965542522090056
Bibliographic databases:
Document Type: Article
UDC: 519.863
Language: Russian
Citation: T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin, “Optimal control of investment in a collective pension insurance model: study of singular nonlinear problems for integro-differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 62:9 (2022), 1473–1490; Comput. Math. Math. Phys., 62:9 (2022), 1438–1454
Citation in format AMSBIB
\Bibitem{BelKonKur22}
\by T.~A.~Belkina, N.~B.~Konyukhova, S.~V.~Kurochkin
\paper Optimal control of investment in a collective pension insurance model: study of singular nonlinear problems for integro-differential equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 9
\pages 1473--1490
\mathnet{http://mi.mathnet.ru/zvmmf11447}
\crossref{https://doi.org/10.31857/S0044466922090058}
\elib{https://elibrary.ru/item.asp?id=49273354}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 9
\pages 1438--1454
\crossref{https://doi.org/10.1134/S0965542522090056}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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