Pressure and heat flux results from the space shuttle/external fuel tank interaction test at Mach numbers 16 and 19

Heat transfer rates and pressures were measured on a 0.0175-scale model of the space shuttle external tank (ET), model MCR0200. Tests were conducted with the ET model separately and while mated with a 0.0175-scale model of the orbiter, model 21-OT (Grumman). The tests were conducted in the AEDC-VKF Hypervelocity Wind Tunnel (F) at Mach numbers 16 and 19. The primary data consisted of the interaction heating rates experienced by the ET while mated with the orbiter in the flight configuration. Data were taken for a range of Reynolds numbers from 50,000 to 65,000 under laminar flow conditions

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

On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling

This paper provides a comparative study of simulation strategies for assessing risk in mortality rate predictions and associated estimates of life expectancy and annuity values in both period and cohort frameworks

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

The management of de-cumulation risks in a defined contribution environment

The aim of the paper is to lay the theoretical foundations for the construction of a flexible tool that can be used by pensioners to find optimal investment and consumption choices in the distribution phase of a defined contribution pension scheme. The investment/consumption plan is adopted until the time of compulsory annuitization, taking into account the possibility of earlier death. The effect of the bequest motive and the desire to buy a higher annuity than the one purchasable at retirement are included in the objective function. The mathematical tools provided by dynamic programming techniques are applied to find closed form solutions: numer-ical examples are also presented. In the model, the trade-off between the different desires of the individual regarding consumption and final annuity can be dealt with by choosing appropriate weights for these factors in the setting of the problem. Conclusions are twofold. Firstly, we find that there is a natural time-varying target for the size of the fund, which acts as a sort of safety level for the needs of the pensioner. Secondly, the personal preferences of the pensioner can be translated into optimal choices, which in turn affect the distribution of the consumption path and of the final annuity

Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach for modelling and projecting mortality

In this paper, we develop accurate approximations for medians of life expectancy and life annuity pure premiums viewed as functions of future mortality trends as predicted by parametric models of the improvement rates in mortality. Numerical illustrations show that the comonotonic approximations perform well in this case, which suggests that they can be used in practice to evaluate the consequences of the uncertainty in future death rates. Prediction intervals based on 5% and 95% quantiles are also considered but appear to be wider compared to simulated ones. This provides the practitioner with a conservative shortcut, thereby avoiding the problem of simulations within simulations in, for instance, Solvency 2 calculations

Optimal investment choices post-retirement in a defined contribution pension scheme

In defined contribution pension schemes, the financial risk is borne by the member. Financial risk occurs both during the accumulation phase (investment risk) and at retirement, when the annuity is bought (annuity risk). The annuity risk faced by the member can be reduced through the “income drawdown option”: the retiree is allowed to choose when to convert the final capital into pension within a certain period of time after retirement. In some countries, there is a limiting age when annuitization becomes compulsory (in UK this age is 75). In the interim, the member can withdraw periodic amounts of money to provide for daily life, within certain limits imposed by the scheme’s rules (or by law). In this paper, we investigate the income drawdown option and define a stochastic optimal control problem, looking for optimal investment strategies to be adopted after retirement, when allowing for periodic fixed withdrawals from the fund. The risk attitude of the member is also considered, by changing a parameter in the disutility function chosen. We find that there is a natural target level of the fund, interpretable as a safety level, which can never be exceeded when optimal control is used. Numerical examples are presented in order to analyse various indices — relevant to the pensioner — when the optimal investment allocation is adopted. These indices include, for example, the risk of outliving the assets before annuitization occurs (risk of ruin), the average time of ruin, the probability of reaching a certain pension target (that is greater than or equal to the pension that the member could buy immediately on retirement), the final outcome that can be reached (distribution of annuity that can be bought at limit age), and how the risk attitude of the member affects the key performance measures mentioned above

The Poisson Log-Bilinear Lee-Carter Model: Applications Of efficient bootstrap methods to annuity analyses

Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. Recent work on the latter has focused on modeling the trend in mortality as a stochastic process. A popular method for modeling death rates is the Lee-Carter model. This methodology has become widely used, and various extensions and modifications have been proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their solvency capital requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company's financial position, expressing the degree to which the liabilities are covered by the assets

Extending the Lee Carter Model: a Three-way Decomposition

In this paper, we focus on a Multidimensional Data Analysis approach to the Lee-Carter (LC) model of mortality trends . In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker 3 model. The suggested methodology allows us to obtain combined estimates for the three modes: i) time, ii) agegroups and iii) different populations. From the results obtained by the Tucker 3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model’s goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares ten European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation

Hard loss of stability in Painlev\'e-2 equation

A special asymptotic solution of the Painlev\'e-2 equation with small parameter is studied. This solution has a critical point $t_*$ corresponding to a bifurcation phenomenon. When $t<t_*$ the constructed solution varies slowly and when $t>t_*$ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and matching procedures