Lee Carter mortality forecasting: application to the Italian population

In this paper we investigate the feasibility of using the Lee-Carter methodology to construct mortality forecasts for the Italian population. We fit the model to the matrix of Italian death rates for each gender from 1950 to 2000. A time-varying index of mortality is forecasted in an ARIMA framework and is used to generate projected life tables. In particular we focus on life expectancies at birth and, for the purpose of comparison, we introduce an alternative approach for forecasting life expectancies on a period basis. The resulting forecasts generated by the two methods are then compared

Coherent modeling of mortality patterns for age-specific subgroups

The recent actuarial literature has shown that mortality patterns and trajectories in closely related populations are similar in some respects and that small differences are unlikely to increase in the long run. The common feeling is that mortality forecasts for individual countries could be improved by taking into account the patterns from a larger group. Starting from this consideration, we apply the three-way Lee–Carter model to a group of countries, by extending the bilinear LC model to a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. From a methodological point of view, there are several issues to deal with when focusing on such kind of data. In the presence of a three-way data structure, several choices on the pretreatment of the data could affect the whole modeling process. This kind of analysis is useful to assess the source of variation in the raw mortality data, before the extraction of the rank-one components by the LC model. The proposed procedure is used to extract an ad hoc time mortality trend parameter for age-specific subgroups. The results show that the proposed strategy leads to a more coherent description of mortality for age-specific subgroups

Longevity-contingent deferred life annuities

Considering the substantial systematic longevity risk threatening annuity providers’ solvency, indexing benefits on actual mortality improvements appears to be an efficient risk management tool, as discussed in Denuit et al. (2011) and Richter and Weber (2011). Whereas these papers consider indexing annuity payments, the present work suggests that the length of the deferment period could also be subject to revision, providing longevity-contingent deferred life annuities

Pension schemes versus real estate

The demographic, economic and social changes that have characterized the last decades, and the dramatic financial crisis that has taken place since 2008, have led to a demand for structural changes in the pension sector and a growing interest in individual pension products. Hence the need, for most elderly people, to liquidate their fixed assets, which are usually the homes in which they live. This highlights products such as reverse mortgages and domestic reversibility plans. Within this context, we propose a contractual scheme where an immediate life annuity is obtained by paying a single-premium in the form of real estate rights (RERs), for example by transferring to an insurer the property title of a house or a similar realty, while keeping its usufruct or a restricted bundle of rights. The level of the installments depends on the fair value of the transferred RER at the contract’s issue, the life expectancy of the insured and the expected growth rate of the real estate market value. The contract design is developed by considering the control of the financial risk inherent in the contract itself, because of the prospective changes in the value of the RERs, and the level of the insurer’s leverage. Finally, we provide some numerical evidence of the proposed contractual structure, in order to compare the level of the installments according to the house return forecasts in different European countries

Shear stress in lattice Boltzmann simulations

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time-dependence of the fluid density in terms of the Reynolds number, Mach number and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.Comment: 15 pages, 4 figures, 2 table

Exponential smoothing methods in pension funding

'Smoothed-market' methods are used by actuaries, when they value pension plan assets, in order to dampen the volatility in contribution rates recommended to plan sponsors. A method involving exponential smoothing is considered. The dynamics of the pension funding process is investigated in the context of a simple model where asset gains and losses emerge as a result of random rates of investment return and where the gains and losses are spread. It is shown that smoothing market values up to a point does improve the stability of contributions but excessive smoothing is inefficient. It is also shown that consideration should be given to the combined effect of the asset valuation and gain and loss adjustment methods. Practical and efficient combinations of gain/loss spreading periods and asset value smoothing parameters are suggested

Pension plan asset valuation

Various asset valuation methods are used in the context of funding valuations. The motivation for such methods and their properties are briefly described. Some smoothed value or market-related methods based on arithmetic averaging and exponential smoothing are considered and their effect on funding is discussed. Suggestions for further research are also made

Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans

The authors consider efficient methods of amortizing actuarial gains and losses in defined-benefit pension plans. In the context of a simple model where asset gains and losses emerge as a consequence of random (independent and identically distributed) rates of investment return, it has been shown that direct amortization of such gains and losses leads to more variable funding levels and contribution rates, compared with an indirect and proportional form of amortization that “spreads” the gains and losses. Stochastic simulations are performed and they indicate that spreading remains more efficient than amortization with simple AR(1) and MA(1) rates of return. Similar results are obtained when a more comprehensive actuarial stochastic investment model (which includes economic wage inflation) is simulated. Proportional spreading is rationalized as the contribution control that optimizes mean square deviations in the contributions and fund levels when the funding process is Markovian and the fund is invested in two assets (a random risky and a risk-free asset). Efficient spreading and amortization periods are suggested for the United States, the United Kingdom, and Canada

The treatment of assets in pension funding

A recent survey of actuarial practitioners in North America shows that smoothed-market actuarial asset values are commonly used in funding valuations of defined benefit pension plans. Four methods of calculating such values are reported in the actuarial literature but only qualitative descriptions of the methods are given. This paper provides mathematical descriptions of the “average of market”, “weighted average”, “deferred recognition” and “write-up” actuarial values. They are shown to be based on either arithmetic or exponential smoothing. Provided the same form of smoothing is used, the four methods are equivalent