Geodesic
Optimal investment and reinsurance strategy
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 6-12

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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. 
@article{VMUMM_2013_2_a1,
     author = {A. N. Gromov},
     title = {Optimal investment and reinsurance strategy},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {6--12},
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     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a1/}
}
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A. N. Gromov. Optimal investment and reinsurance strategy. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 6-12. http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a1/