Longevity risk modelling with application to insurer longevity risk based capital stress margins

A thesis submitted for the degree of Doctor of Philosophy (PhD) in Actuarial StudiesFuture mortality rates are uncertain and the risk that estimated mortality rates will be higher than observed rates has negative financial implications for providers of living benefitts including life annuities and pensions. This thesis studies time trends and cohort trends in mortality rates to determine the number of factors that drive mortality changes. An econometric analysis of mortality improvements is used to give a clearer picture of the stochastic nature of mortality rates in a lower dimensional data space as this thesis uses co integration analysis for dimension reduction.A multi-country analysis of standardized mortality rates finds evidence of stochastic trends and a significant number of common factors. However, no evidence of common stochastic trends is found. An analysis of Australian mortality rates establishes there are non-stationary and stationary mortality rates by age. The common stochastic trends across age-groups which are exhibited within the Australian data lead to the characterization of mortality rates using a stochastic trend model. Dimension reduction is performed using the Heligman and Pollard (1980) parametric mortality model. The trends in the data are reflected using flexible Vector Autoregressive (VAR) models allowing for correlation between the estimated Heligman and Pollard model parameters. Bayesian Vector Autoregressive (BVAR) models which additionally quantify parameter risk are shown to significantly improve the forecast accuracy when fitting the developed HP-BVAR model to data from 1946-1995 and then comparing its out-of-sample forecasts to observed data from 1996-2007 for Australian mortality rates. Allowing for parameter uncertainty shows it to be a signicant component of total risk since the results are realistic probabilistic forecasts. The HP-BVAR model is applied to the calibration of the longevity stress margin of the life insurance capital charge. The structure and magnitude of the current simplification by APRA result in a longevity stress margin that is found to be too prudent and too generalised. An alternative age-dependent simplification is proposed.Future mortality rates are uncertain and the risk that estimated mortality rates will be higher than observed rates has negative financial implications for providers of living benefit ts including life annuities and pensions. This thesis studies time trends and cohort trends in mortality rates to determine the number of factors that drive mortality changes. An econometric analysis of mortality improvements is used to give a clearer picture of the stochastic nature of mortality rates in a lower dimensional data space as this thesis uses co integration analysis for dimension reduction.A multi-country analysis of standardized mortality rates fi nds evidence of stochastic trends and a signifi cant number of common factors. However, no evidence of common stochastic trends is found. An analysis of Australian mortality rates establishes there are non-stationary and stationary mortality rates by age. The common stochastic trends across age-groups which are exhibited within the Australian data lead to the characterization of mortality rates using a stochastic trend model. Dimension reduction is performed using the Heligman and Pollard (1980) parametric mortality model. The trends in the data are reflected using flexible Vector Autoregressive (VAR) models allowing for correlation between the estimated Heligman and Pollard model parameters. Bayesian Vector Autoregressive (BVAR) models which additionally quantify parameter risk are shown to signifi cantly improve the forecast accuracy when fi tting the developed HP-BVAR model to data from 1946-1995 and then comparing its out-of-sample forecasts to observed data from 1996-2007 for Australian mortality rates. Allowing for parameter uncertainty shows it to be a signi cant component of total risk since the results are realistic probabilistic forecasts. The HP-BVAR model is applied to the calibration of the longevity stress margin of the life insurance capital charge. The structure and magnitude of the current simpli fication by APRA result in a longevity stress margin that is found to be too prudent and too generalised. An alternative age-dependent simpli fication is proposed

Evaluation of the effectiveness of cooperative learning structures in improving students\u27 performance

In a desperate attempt to improve high school classroom performances, recently, schools have begun to move towards incorporating cooperative learning strategies into their classrooms. Generally, cooperative learning strategies can be described as the use of small groups to encourage learners work together and accomplish shared goals and subsequently maximize theirs and others’ potential. In an attempt to evaluate the effectiveness of this strategy on classroom learning, this study compares the gains in means of scores between a group taught using cooperative learning strategies and another group taught using non-cooperative learning strategies. Fifty-three students taking Algebra I were given a pretest before administering this strategy then a posttests afterwards to determine the normalized gain based on the Hake equation. Thirty-one students participated in cooperative learning out of which 77% showed a net mean positive gain whereas, the 22 students in the non-cooperative group had a positive gain of 54%. Comparison of these results did not indicate any statistical significance between the two groups. However, it was observed that students who worked in cooperative groups were more engaged, more responsible in completing group assignments and more organized while working in their respective groups. These results may encourage the practice of cooperative learning strategies in a high schoollevel setting

A moment for Africa

Speech by George N. NjengaSpeech by George N. Njeng

Matrimony: A key element in the demographic system of Modern Europe

In this paper, I summarize Moreno’s work cited above. This summary discusses the factors affecting human natural fertility and also considers European experience during the Modern period. This has been made possible thanks to the advancement of the science of human fertility over the last 60 years. Some theories on “demographic Change” in the 1950’s and 60’s, proposed that human fertility, before ‘the modern transition’, had reached its “biological limit” and the only fundamental variable regulating its changes in the short, medium and long term was ‘mortality’.1 No one doubts that past mortality levels were higher than our contemporary experience. Besides, variations in mortality, be they ordinary or extraordinary (as a result of wars, hunger and infection), played a greater role than presently in regulating population increase. However, it is one hypothesis to admit that mortality played a crucial role in population demographics and another to propose that ultimately variations in population demographics depended exclusively on changes in mortality. Was that really the case? Were there other factors that significantly affected population growth? More, how did western civilization regulate fertility before the demographic transition?

User pattern analysis of mobile payment systems: evidence from the streets of Nairobi

Paper presented at ICT conference of 2009.This paper sets to analyze the utilization trends of mobile based payment systems in Kenya. A user perception analysis model is employed to provide a suitable investigation framework

How do Vocational Teachers Learn? Formal and Informal Learning by Vocational Teachers in Kenya

Context: Participation in Continuing Professional Development (CPD) supports the development of vocational teacher competencies. However, it is often not clear what learning methods vocational teachers use in their CPD. This study therefore investigated the CPD practices of vocational teachers in Kenya, with a specific focus on the formal and informal learning methods used. Approach: The study used a questionnaire survey to collect data from TVET teachers randomly drawn from six Technical and Vocational Colleges in Kenya's Nairobi Metropolitan Area. Descriptive and inferential analysis of the data was used to determine how frequently different learning methods are used and to identify associations between CPD practices and teacher characteristics.Findings: TVET teachers in Kenya were found to use different learning methods depending on the availability of the learning methods and the learning goals teachers have. Formal academic learning and discussions with colleagues are frequently used while collaborative learning methods and practice-based learning activities are less frequently used. Rarely used are written reflections about practice and its outcomes. Despite viewing Lecturer Industrial Attachment (LIA) as important and therefore wishing to attend LIA, more than a third of the participants indicated that they had never attended LIA. The use of professional literature is restricted to text books with limited use of primary and secondary literature. CPD activities such as mentoring, supervising other teachers, and school visits were found to form a unique category of CPD activities that is more frequently used by teachers with administrative responsibilities. Conclusion: The limited use of active learning methods that involve critical evaluation of practices and their outcomes risks limiting the ability of vocational teachers in Kenya to transform and adopt better practices. It is recommended that vocational teachers in Kenya are encouraged to adopt a broad conception of teacher CPD that embraces collaborative, reflective, and practice-based learning.

Implementation of a Low Cost Micro Electro Mechanical Systems Inertial Navigation Solution

The purpose of this study is to develop a low cost navigation solution for General Aviation (GA) aircraft and flight testing aircraft. This low cost solution uses a Global Positioning System (GPS) coupled with an Inertial Navigation Solution (INS) to provide a more accurate, stable navigation solution that can be acceptable for aircraft navigation. Lab VIEW was utilized to perform data acquisition and computation. LabVIEW was the backbone software to perform real time computation. MATLAB ® Simulink ® was used to plot graphs for final analysis of the code. A software Kalman Filter was utilized to provide signal stability and signal continuity. This study will be utilized as a preliminary step towards the development of inexpensive alternate methods of aircraft navigation for GA and flight testing

The Feudal system in Medieval Europe (7th-14th Century A.D.)

This document is a summary of the European feudal system in the medieval ages from an excerpt by: SB Clough y RT Rapp, Historia Economica de Europa. El desarrollo Económico de la Civilización Occidental, Barcelona, Omega, 1986, Cap.3.This document is a summary of the European feudal system in the medieval ages from an excerpt by: SB Clough y RT Rapp, Historia Economica de Europa. El desarrollo Económico de la Civilización Occidental, Barcelona, Omega, 1986, Cap.3.This document is a summary of the European feudal system in the medieval ages from an excerpt by: SB Clough y RT Rapp, Historia Economica de Europa. El desarrollo Económico de la Civilización Occidental, Barcelona, Omega, 1986, Cap.3.This document is a summary of the European feudal system in the medieval ages from an excerpt by: SB Clough y RT Rapp, Historia Economica de Europa. El desarrollo Económico de la Civilización Occidental, Barcelona, Omega, 1986, Cap.3

Men and Women - a sociological vision of differences: the case of Spain

A summary of Almárcegui, A. Moreno, Hombres y Mujeres: Una Visión Sociológica de sus Diferencias: El Caso de España: en la Obra de Enciso, Agustín,“Mas Allá de la División del Trabajo: (2007): Pamplona