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We recall how a standard semi-Markov framework can be applied for the modelling of general life insurance with-profit contracts. Within this setting, we give an introduction to principles used in Denmark for market-based valuation of life insurance liabilities; in particular this involves so-called "individual bonus potentials".
Methods for calculating cash flows and expected present values in an economic environment are discussed. The main tools are well-established generalised versions of Thiele's differential equation for the state-wise reserves, and Kolmogorov's differential equations for the transition probabilities. We discuss methods for solving these equations, which seem useful in practice.
The second part of the talk deals with so-called mortality-derivatives, which have been offered recently by various financial institutions. We focus on mortality-swaps and suggest to apply quadratic criteria for determining the optimal choice of such contracts.
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