An annuity reserve is a prediction of a claimant’s loss of earnings in the future. Annuity reserves are a significant part of P/C insurers’ technical provision in Finland. The majority of P/C annuities are caused by work-related accidents or traffic accidents. 

Any P/C insurer, who is responsible of an annuity, carries financial risk. If reality differs from prediction, annuities’ costs might exceed reserves and the insurer must pay the difference from its own capital. Annuity reserving incurs risks of three main type; revision risk, interest rate risk and longevity risk. Inflation risk is neutralized by Finnish legislation, because yearly index increases of annuities are funded outside P/C insurers own financials according to a ‘pay as you go’ scheme. 

Revision risk reflects the uncertainty of future annuity payments. In particular, ‘part time annuities’ contain revision risk. These annuities might be revised and become ‘full time annuities’ if the circumstances of a claimant change. Interest rate risk reflects the uncertainty of future risk-free returns. When setting annuity reserves, discounting is used to evaluate cash flows. Discounting represents risk-free returns from investment markets. Longevity risk reflects the uncertainty of remaining lifetime. When setting annuity reserves, assumption of claimants’ survival probabilities are made. 

In this paper, longevity risk is analysed mathematically. A model is defined that aims to illustrate long-term stochasticity of mortality. The model is applied to simulate possible future scenarios of survival probabilities, and therefore possible outcomes of annuity. 

Main goals of this paper are to portray annuity uncertainty and to present mathematical approach for longevity risk modeling

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