In the work, which is at the junction of financial and actuarial mathematics, we study methods of quantitative calculations of premiums and reserves for flexible insurance schemes (equity-linked insurance schemes). The necessary information and description of the main approaches (actuarial reserve, static and dynamic hedging) to the calculation of such innovative schemes are given. Particular attention is paid to the most important method - the method of dynamic hedging, which is analyzed in detail both for the most studied case of full markets (black-Scholes model) and for the case of incomplete markets (generalized Bachelier model with stochastic volatility).