We develop a pair of risk measures for the universe of health and longevity products that includes life insurance, annuities, and supplementary health insurance. Health delta measures the differential payoff that a policy delivers in poor health, while mortality delta measures the differential payoff that a policy delivers at death. Optimal portfolio choice simplifies to the problem of choosing...

The market for private life annuities is characterised by adverse selection, that is, contracts offer lower than fair payoffs to individuals with low life expectancy. Moreover, life expectancy and income have been found to be positively correlated. The paper shows that a linear tax on annuity payoffs, which raises more revenues from long-living individuals than from short-living, represents an ...

that if we place money in the bank that pays this interest and withdraw the amount A every year, we will get exactly 0 after n-th withdrawal. Knowing q enables us to make decisions about whether to invest in this annuity or not: e.g., if this q is smaller than the actual bank's interest rate 90, then it is better to leave the money in the bank; if q is larger than qo, then it is better to inves...

In connection with a problem posed by Kijima and Wong [11], we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique which permits to obtain a first order approximation formula f...

Over the next years, the ageing profile of the UK population will lead to a sharp increase in the volumes of pension annuity sales. Every individual that participates in a defined contribution occupational or a personal pension scheme is obliged to convert the capital accumulated into a regular post-retirement income by purchasing an annuity before the age of 75. To ensure a more competitive ma...

For decades the debate on pensions has focused on the “accumulation phase” of the life-cycle. Many specific research topics have been explored as this literature has developed. However, they were all in one way or another concerned by the adequacy of saving. In other words, the main focus of the existing literature has been on the question of setting enough resources aside to keep the flow of c...

When formulating life-cycle models in economics, the economic profession has focused on restrictions on theory from empirical data on consumption, wealth, and leisure. This has yielded substantial progress. However, central aspects of these models must still be regarded as controversial. Two such open questions are how to model families and how to model and measure within-family altruism. The b...

Even in case of the Brownian motion as most natural rate of return model it appears too difficult to obtain analytic expressions for most risk measures of constant continuous annuities. In literature so-called comonotonic approximations have been proposed but these still require the evaluation of integrals. In this paper we show that these integrals can sometimes be computed, and we obtain expl...