  Calculation of an optimal tariff is a principal challenge for pricing
actuaries. In this contribution we are concerned with the renewal insurance
business discussing various mathematical aspects of calculation of an optimal
renewal tariff. Our motivation comes from two important actuarial tasks, namely
a) construction of an optimal renewal tariff subject to business and technical
constraints, and b) determination of an optimal allocation of certain premium
loadings. We consider both continuous and discrete optimisation and then
present several algorithmic sub-optimal solutions. Additionally, we explore
some simulation techniques. Several illustrative examples show both the
complexity and the importance of the optimisation approach.
