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

Self-selection and risk sharing in a modern world of lifelong annuities - Abstract of the London Discussion

This abstract relates to the following paper: Gerrard, R., Hiabu, M., Kyriakou, I. and Nielsen, J. P. (2018) Self-selection and risk sharing in a modern world of lifelong annuities ‐ Abstract of the London Discussion. British Actuarial Journal. Cambridge University Press, 23. doi: 10.1017/S135732171800020X

Self-selection and risk sharing in a modern world of life-long annuities

Communicating a pension product well is as important as optimising the financial value. In a recent study, we showed that up to 80% of the value of a pension lump sum could be lost if customer communication failed. In this paper, we extend the simple customer interaction of the earlier contribution to the more challenging lifetime annuity case. Using a simple mobile phone device, the pension customer can select the life-long optimal investment strategy within minutes. The financial risk trade-off is presented as a trade-off between the pension paid and the number of years the life-long annuity is guaranteed. The pension payment decreases when investment security increases. The necessary underlying mathematical financial hedging theory is included in the stud

Measures of Niche Overlap, II

An axiomatic basis for the construction of measures of niche overlap is analysed, and its implications are discussed, with particular reference to the more commonly used measures. A method of establishing that a measure of overlap complies with the axioms is put forward, making possible the construction of families of new measures. Certain extremal measures of overlap are also identifie

On the worst and least possible asymptotic dependence

Multivariate extremes behave very differently under asymptotic dependence as compared to asymptotic independence. In the bivariate setting, we are able to characterise the extreme behaviour of the asymptotic dependent case by using the concept of the copula. As a result, we are able to identify the properties of the boundary cases, that are asymptotic independent but still have some asymptotic dependent features. These situations are the most problematic in statistical extreme, and, for this reason, distinguishing between asymptotic dependence and asymptotic independence represents a difficult problem. We propose a simple test to resolve this issue which is an alternative to the procedure based on the classical coefficient of tail dependence. In addition, we are able to identify the worst/least asymptotic dependence (in the presence of asymptotic dependence) that maximises/minimises the probability of a given extreme region if tail dependence parameter is fixed. It is found that the perfect extreme association is not the worst asymptotic dependence, which is consistent with the existing literature. We are able to find lower and upper bounds for some risk measures of functions of random variables. A particular example is the sum of random variables, for which a vivid academic effort has been noticed in the last decade, where bounds for a sum of random variables are sought. It is numerically shown that our approach provides a great improvement of the existing methods, which reiterates the sensible conclusion that any additional piece of information on dependence would help to reduce the spread of these bounds

Measures of Niche Overlap, I

Many methods of measuring niche overlap have been proposed, such as those of Renkonen, Morisita, and Horn. In this paper, conditions are put forward which overlap indices should reasonably be expected to satisfy. A general description of a good index is given, which covers as special cases those of the well-known indices which satisfy all the conditions. A mixture of the Renkonen and van Belle & Ahmad indices is suggested, as it has many desirable properties. The problem of estimating overlap from data is discussed briefl

Simulations of a lattice model of two-headed linear amphiphiles: influence of amphiphile asymmetry

Using a 2D lattice model, we conduct Monte Carlo simulations of micellar aggregation of linear-chain amphiphiles having two solvophilic head groups. In the context of this simple model, we quantify how the amphiphile architecture influences the critical micelle concentration (CMC), with a particular focus on the role of the asymmetry of the amphiphile structure. Accordingly, we study all possible arrangements of the head groups along amphiphile chains of fixed length $N=12$ and 16 molecular units. This set of idealized amphiphile architectures approximates many cases of symmetric and asymmetric gemini surfactants, double-headed surfactants and boloform surfactants. Consistent with earlier results, we find that the number of spacer units $s$ separating the heads has a significant influence on the CMC, with the CMC increasing with $s$ for $s<N/2$. In comparison, the influence of the asymmetry of the chain architecture on the CMC is much weaker, as is also found experimentally.Comment: 30 pages, 17 fgure

Hedging of Asian options under exponential Lévy models: computation and performance

In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Lévy model by deriving backward recursive integrals for the price sensitivities of the option. The procedure is applied to the analysis of the performance of the delta and delta-gamma hedges in an incomplete market; particular attention is paid to the hedging error and the impact of model error on the quality of the chosen hedging strategy. The numerical analysis shows the impact of jump risk on the hedging error of the option position, and the importance of including traded options in the hedging portfolio for the reduction of this risk

Limiting Family Size Through the Sufficient Provision of Basic Necessities and Social Services: The Case of Pasay, Eastern Samar, and Agusan Del Sur

The socio-economic quandaries of rapid population growth and poverty have always been coupled. It is evident that the poorest households are those who have larger family size. Consequently, these households have to support more people with fewer resources, making the family live a life of inherited poverty. With this, the state has been on the pursuit of looking for solutions such as the Reproductive Heath (RH) Bill to address rapid population growth and eventually poverty. However, the Roman Catholic Church (RCC) condemns the RH Bill because it is contradictory to Catholic principles. For this reason, we will explore other possibilities to limit family size by highlighting whether the availability of water, electricity, decent housing, sustainable income, employment, and other welfare enhancing programs limits family size. By showing whether the provision of these basic sustenance affects family size via the Maximum Likelihood Estimation (MLE) procedure, it is then possible to propose an alternative solution other than the use of contraceptives. Likewise, the government can improve on its socio-economic policies that will address the problem of overpopulation. Results have shown that Pasay, Eastern Samar, and Agusan Del Sur responded differently to various stimuli such as living conditions, educational attainment, employment status, as well as government-funded programs among others insofar as population dynamics is concerned. This suggests a need to peer into the distinction of each region’s socioeconomic context and underlying psyche. The milieu within which an individual resides may greatly influence his rational calculus and decision-making process. Also, beyond tailoring-fitting population control programs, there is also a need to calibrate policies based on relevant socioeconomic, political, and cultural nuances each region may possess