Abstract:In this paper, we consider the Markovian model for the actuarial modelling of health insurance policies modified by the inclusion of durational effects (the time elapsed since entering a given state) on the aggregate payment streams, where the force of interest is a diffusion process. We derive differential equations for the first moment of the present value of the aggregate amount of benefits. We also give two examples to illustrate our results.

Abstract:As the principal decision-makers in retirement funds, trustees have a number of duties placed upon them including a duty of care, a duty of impartiality, a duty to avoid and manage conflicts of interest, a duty to act in accordance with the purpose of the fund and a duty of accountability. Decision-making by trustees and the actuaries that assist them can be informed by considering various ethical theories. This paper reviews the theory of right action, virtue theory and the ethics of care, together with the theory of justice, and interprets the duties of trustees and actuaries in terms of these theories. After consideration of other frameworks for ethical decision-making, a six-step decision-making framework based on the actuarial control cycle is developed to provide an initial attempt to formalise the process
of ethical decision-making in South African retirement funds. This framework is applied to case studies involving the review of surplus apportionment, an investment policy statement, the distribution of death benefits, and annuitisation options. The case studies illustrate that, although the framework itself does not provide ethical solutions, it assists trustees, and the actuaries who advise them, with the process of making an ethical decision.

For the last five years, in March and October, I have found myself standing in the conference room of a Stellenbosch wine farm or a Sandton hotel, looking out at 20 to 24 bright, young and expectant faces. I say expectant, but perhaps many of them are thinking “Really! Two days on Professionalism”. You see, the Actuarial Society of South Africa—that is you—have placed into these hands, and the six hands of my co-coordinators, and the ten hands of our guest presenters, the responsibility of turning these individuals into professionals.

Abstract:This paper aims to introduce jump tests to the actuarial community. In actuarial science, semimartingales are extensively used in the models for interest rates, options, variable annuities and equity-linked annuities. Those models usually assume without justification that the underlying asset process follows a continuous stochastic process such as a geometric Brownian motion, for the market data sometimes tell a different story. Choosing between a continuous model and a model with jumps is not only important for pricing of insurance products but also crucial for implementing other post-sales risk management measures such as dynamic liability hedging. A test for jumps allows actuaries to rigorously test whether the underlying asset process has jumps, which is the first critical step in model selection. The ability to
conduct the test should thus belong to the repertoire of every expert and practitioner working in this field. In this paper, we review several major tests for jumps, describe their advantages and disadvantages, and offer suggestions for their implementation. We also implement several tests using real data, enabling practitioners to apply these tests in their work.

Abstract:A methodology for the assessment of the probable maximum loss associated with an earthquake is described and applied to the Cape Town central business district. The calculations are based on the effect of the two largest earthquakes that occurred in Milnerton in 1809 and Ceres–Tulbagh in 1969. The investigation concludes that if buildings and infrastructure in an area follow the SANS Standard 10160 for seismic loading of 0.1g, they are exposed to significant seismic risk. The main purpose of
this research is not the accurate quantification of expected losses to Cape Town’s infrastructure, but to raise awareness between civil engineers, the insurance industry and disaster management agencies that seismic hazard is an issue in South Africa and must be considered as a potential threat to its residents and infrastructure.

Abstract: The purpose of this study is to investigate the pricing of variable annuity embedded derivatives using a suitably refined model for the underlying assets, in this case the Johannesburg Securities Exchange FTSE/JSE All Share Index (ALSI). This is a practical issue that life insurers face worldwide in the management of embedded derivatives. We consider the Variance-Gamma (VG) framework to model the underlying data series. The VG process is useful in option pricing given its ability to model higher moments, skewness and kurtosis and to capture observed market dynamics. The framework is able to address the inadequacies of some deterministic pricing approaches used by life insurers, given the increasing complexity of the option-like products sold

Abstract: This paper investigates catastrophe risk for South African life insurers by considering the additional deaths that could arise from a 1-in-200 year mortality shock. Existing South African academic research on catastrophic risk has mostly focused on property losses and the resulting impact on property insurance companies. Life catastrophe risks have not been extensively modelled in a South African context. Local research would be beneficial in terms of quantifying these catastrophic risks for South African life insurers, and would assist firms when assessing their own catastrophe mortality solvency requirements under the new Solvency Assessment and Management (SAM) regime by providing a summary of data relating to various past catastrophes. In this paper we model a wide range of catastrophes to assess such mortality risk faced by life insurance companies in South Africa. An extensive exercise was undertaken to obtain data for a wide range of catastrophes and these data were used to derive severity and frequency distributions for each type of catastrophe. Data relating to global events were used to supplement South African data
where local data were sparse. Data sources included official government statistics, industry reports and historical news reports. Since, by nature, catastrophic events are rare, little data are available for certain types of catastrophe. This means there is a large degree of uncertainty underlying some of the estimates. Simulation techniques were used to derive estimated distributions for the potential number of deaths for particular catastrophic events. The calculated overall shock for the national population was 2.6 deaths per thousand, which was lower than the SAM Pillar 1 shock of 3.2 deaths per thousand for the same population

Abstract:The aim of this paper is to investigate the expenditure incurred by health insurers arising from the provision of benefits during the 12 months preceding a beneficiary’s death. Concern is expressed in parts of the international literature about the extent of resources directed towards those at the end of life, particularly given increased longevity and technological advancement. Two types of investigation are discussed: first, a comparison of costs in the last year of life with costs in earlier years prior to death and, second, a comparison of decedent and survivor costs within a calendar year. Within each investigation, further detailed analyses were performed with particular emphasis on the distribution of last-year-oflife costs by age and category of expenditure. A South African dataset is used to illustrate the suggested methodology. The average cost in the last year of life is found to be 3.3 times higher than the average cost in the second last year of life. Average decedent costs are found to be 17.85 times higher than average survivor costs in 2012, on a risk-adjusted basis. The majority of these costs (83.35% in 2012) form part of the Prescribed Minimum Benefit package.