Financial and Insurance Formulas

Modelling Longevity Risk in the Context of Central Statistical Office Population Projections for Poland to 2050

“…If a pension system is based on the fund principle we must decide how much to "save" annually during the accumulation phase and how much to "spend" annually during the decumulation (annuity) phase (Cipra 2010). In view of the many random aspects, the best approach is similar to that applied in modern finance: Value at Risk, whereby the highest loss that can occur with a given probability (tolerance) is calculated.…”

“…Its obverse is the probability of ruin (the probability of an unsustainable pension). This is closely connected with the practise of pension planning or of managing the risk of pensions (Cipra 2010). In terms of internal models, the Solvency II guidelines propose using Value at Risk to compute the capital required when an insurer prefers to develop its own framework for risk assessment (Barrieu et al 2012).…”

Econometric Model of the Czech Life Insurance Market

“…Links among these economic data can be investigated through econometric modelling based on actuarial theory (see e.g. Cipra, 2010). On the other hand, one could possibly extend the introduced model into a more general form including other insurance or economic variables.…”

“…In particular, Solvency II is a new regulatory schedule that can make use of insurer's internal models including stress tests, see e.g. Cipra (2010) or Sandström (2006). In the considered context, one can apply different general approaches to scenario analysis: (i) analysis of deterministic scenarios simply based on given expert (optimistic or pessimistic) values of strictly exogenous variables, (ii) analysis of random scenarios generated via some econometric models or (iii) their combination.…”

Some Annuity Problems in the Framework of Czech Pension Systems

“…In view of many random aspects the best approach is similar to the one applied in modern fi nance, namely the Value-at-Risk (VaR, see e.g. Cipra, 2010), when one calculates the highest loss which can occur with a given probability (tolerance). In the pension context it must be modifi ed to the probability that the retired person will not be "ruined" before the moment of death (such a probability can be called the probability of sustainable pension) while its complement to 1 is the probability of ruin (or the probability of unsustainable pension).…”