Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2013, Number 2, Pages 6–12 (Mi vmumm386)  
Mathematics

Optimal investment and reinsurance strategy

A. N. Gromov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: An insurance company is modelled by a compound Poisson process and it is assumed that the company has a possibility to purchase an excess of loss reinsurance defined by retention level as well as invest its surplus into a risky asset described by the Black–Scholes model. An optimal survival probability is derived as a solution to the corresponding Hamilton–Jacobi–Bellman equation. It is proved that any increasing solution to the Hamilton–Jacobi–Bellman equation defines the optimal strategy.
Key words: survival probability, excess of loss reinsurance, Black–Scholes model, Hamilton–Jacobi–Bellman equation.
Received: 16.04.2012
English version:
Moscow University Mathematics Bulletin, 2013, Volume 68, Issue 2, Pages 87–92
DOI: https://doi.org/10.3103/S0027132213020022
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: A. N. Gromov, “Optimal investment and reinsurance strategy”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, no. 2, 6–12; Moscow University Mathematics Bulletin, 68:2 (2013), 87–92
Citation in format AMSBIB
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\jour Moscow University Mathematics Bulletin
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