Optimal strategy of reinsurance and investment / A. N. Gromov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 2. P. 6-12 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
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.}