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[en] The well-known problem of finding explicit formulas for the expected return and risk of portfolios with general commission is completely solved. It is assumed that the commission depends on the asset and the asset position, and on whether the given position is opened or closed. For portfolios with only the budget constraint and initial commission, we prove that the function of expected portfolio return and portfolio variance function are bounded.
[en] We study nonlinear models of the expected number of unreported claims by year end with a randomized probability of claims to be reported. According to the developed simulation models the models with randomized probability more adequately describe the actual arrival process of insurance claims.