Optimal Insurance and Investment Strategies in Individual Risk Models with Background Risks

In the presented paper, a one-stage problem of simultaneous finding an optimal insurance and investment portfolio in the presence of background risks is studied. The goal functional is a functional of Markovitz type which depends on the first two moments of the final capital. It is shown that the optimal insurance necessarily belongs to a class of stop loss insurances, equations determining parameters of the stop loss insurance and investment portfolio are derived. A numerical example illustrating the theoretical results is given.