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When long-term savers plan for retirement they need to know their investment prospects in terms of real income (Merton, 2014). While inflation has traditionally been considered as a complication in financial analysis and financial practise, we obtain enhanced predictability and model fit if the real returns are targeted in conjunction with earnings-by-price minus inflation as predictor. For this latter case, we propose an investment strategy of updating the simple classical Merton proportion as we go along. This simple strategy is very close to the complicated theoretically optimal solution but has comparably much lower parameter uncertainty.

In this chapter the problems of the prevalence of esophageal cancer and the distribution of mortality rates from this disease are considered in the countries of Central and Eastern Europe. The rates of mortality from esophageal cancer are analyzed by statistical methods, econometrics, spatial and time series analysis. A study is carried out of the features of the tendencies of mortality rates from esophageal cancer in six EU countries and in Ukraine. The problems of the prevalence of esophageal cancer and the spatial distribution of mortality rates from this disease are considered using as examples the NUTS 2 regions in six countries of Central and Eastern Europe (Austria, Germany, the Czech Republic, Poland, Slovakia and Hungary). The spatial distribution of the rates of mortality from esophageal cancer is analyzed. It allows us to determine more and less epidemiologically affected regions and to carry out more detailed studies on the link between the mortality rates from esophageal cancer and various factors. It is emphasized that various factors, such as the environmental situation, socio-demographic characteristics of the population, culture and nature of nutrition, the general health status of the population, the availability of resources and the level of healthcare in the region should be took into account for development of complex of treatment and care and for the programs for the prevention of prevalence of esophageal cancer.

The paper shows how to reform the platform of pension products so that pension savers, professional financial advisors, actuaries and investment experts intuitively understand the underlying financial risk of the optimal investment profile. It is also pointed out that an excellent optimal investment strategy can destroy the future expected utility of a pension saver if the financial communication is wrong. It is shown that a simple system with an upper and a lower bound, originally inspired by Merton (2014), which can be executed easily using fintech, can replace complicated power utility optimization for the pension saver so that everyone can exactly understand the amount of financial risk taken. The paper focuses on investing money as a lump sum because being able to communicate the associated financial risk can serve as the first step towards communicating more complex pension saving structures.

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 life-long annuities. British Actuarial Journal. Cambridge University Press, 23. doi: 10.1017/S135732171800020X.

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 study.

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 briefly

Background: There are different approaches to the assessment of the severity of trauma in a victim and to the provision of specialized health care. Some of them are based on the development of scales and logistic models, using expert systems or statistical methods, to assess the severity of injury and the probability of a particular outcome. This article presents the results of a study on the feasibility of developing and applying various statistical models in order to predict the outcome in the case of different types of trauma, based on data on the status of victims with severe trauma. Patients and methods: We present selected information about 373 victims, admitted and treated at the Department of Traumatic Shock of the GI «V.T. Zaycev Kharkiv Research Institute of General and Emergency Surgery» of NAMS of Ukraine; the records, which relate to patients with severe and combined trauma, were made between 1985 and 2015. The initial database contained 263 victims who had positive outcomes (survived), while 110 had fatal outcomes. Most of the patients presented with an open trauma (285 cases), then there were 80 cases with a closed injury and only 8 cases with a combined injury. Results: To estimate the probability of the outcome for various types of trauma we have developed a predictive model, based on a logistic relationship. Categorical variables, indicating the presence or absence of various types of trauma, were used in the model. Information about the eventual outcome for a given victim with the indicated type of trauma was used as the dependent variable. The logit model which we obtained has a high predictive accuracy in predicting positive outcomes. Thus, based on the a posteriori analysis, 92% of cases in which victims survived were correctly recognized by the model. In view of the fact that abdominal trauma is the commonest of all trauma mechanisms, we constructed a predictive model to estimate the probability of various outcomes in the case of abdominal trauma or injury to certain organs of the abdominal cavity. Linear discriminant functions were developed by us and used for the classification of possible outcomes depending on the condition of the victim and the resuscitation measures carried out. The model presented has a high predictive accuracy: on the basis of a posteriori analysis using data of discriminant functions, correct conclusions were drawn in 90% of cases when there was a positive outcome, and in 75% of cases when the outcome was fatal. Conclusion: We conclude that it is reasonable to use the statistical model developed, along with other qualitative and quantitative methods of prognostic determination of outcomes for victims with severe injuries. As different models have different predictive accuracy and require the provision of different information, it is necessary to use a sufficiently large number of techniques to derive accurate predictions and to choose the right tactics for diagnosis and treatment.

In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Levy 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.

Modeling and forecasting extreme co-movements in financial market is important for conducting stress test in risk management. Asymptotic independence and asymptotic dependence behave drastically different in modeling such co-movements. For example, the impact of extreme events is usually overestimated whenever asymptotic dependence is wrongly assumed. On the other hand, the impact is seriously underestimated whenever the data is misspecified as asymptotic independent. Therefore, distinguishing between asymptotic independence/dependence scenarios is very informative for any decision-making and especially in risk management. We investigate the properties of the limiting conditional Kendall’s tau which can be used to detect the presence of asymptotic independence/dependence. We also propose nonparametric estimation for this new measure and derive its asymptotic limit. A simulation study shows good performances of the new measure and its combination with the coefficient of tail dependence proposed by Ledford and Tawn (1996, 1997). Finally, applications to financial and insurance data are provided.

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.

In this article the problems of the prevalence of esophageal cancer and the spatial distribution of mortality rates from this disease are considered using as examples the NUTS 2 regions in six countries of Central and Eastern Europe (Austria, Germany, the Czech Republic, Poland, Slovakia and Hungary). The rates of mortality from esophageal cancer are analyzed by statistical methods and by spatial econometrics. A study is carried out of the features of the spatial distribution of the rates of mortality from esophageal cancer. It allows us to determine more and less epidemiologically affected regions and to carry out more detailed studies on the link between the mortality rates from esophageal cancer and various factors, such as the environmental situation, socio-demographic characteristics of the population, culture and nature of nutrition, the general health status of the population, the availability of resources and the level of healthcare in the region. By means of the multifactor regression model we forecast the rates of mortality from esophageal cancer, taking into account characteristics of the countries, the dynamics of the number of patients with diseases of the esophagus and the general time trend.

In this article the problems of the prevalence of esophageal cancer and the spatial distribution of mortality rates from this disease are considered using as examples the NUTS 2 regions in six countries of Central and Eastern Europe (Austria, Germany, the Czech Republic, Poland, Slovakia and Hungary). The rates of mortality from esophageal cancer are analyzed by statistical methods and by spatial econometrics. A study is carried out of the features of the spatial distribution of the rates of mortality from esophageal cancer. It allows us to determine more and less epidemiologically affected regions and to carry out more detailed studies on the link between the mortality rates from esophageal cancer and various factors, such as the environmental situation, socio-demographic characteristics of the population, culture and nature of nutrition, the general health status of the population, the availability of resources and the level of healthcare in the region. By means of the multifactor regression model we forecast the rates of mortality from esophageal cancer, taking into account characteristics of the countries, the dynamics of the number of patients with diseases of the esophagus and the general time trend.

We solve a portfolio selection problem of an investor with a deterministic savings plan who aims to have a target wealth value at retirement. The investor is an expected power utility-maximizer. The target wealth value is the maximum wealth that the investor can have at retirement. By constraining the investor to have no more than the target wealth at retirement, we find that the lower quantiles of the terminal wealth distribution increase, so the risk of poor financial outcomes is reduced. The drawback of the optimal strategy is that the possibility of gains above the target wealth is eliminated.