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South African Actuarial Journal Volume 15 (2015)


A scenario approach to estimate the maximum foreseeable loss for buildings due to an earthquake in Cape Town

Authors: A Kijko, A Smit and N van de Coolwijk

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 0.1 g, 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.
Keywords:Probable maximum loss (PML); seismic risk; hazard; expected damage; Cape Town; short-term
insurance

A Scenario approach to estimate the maximum foreseeable loss for buildings due to an earthquake in Cape Town

 

An actuarial perspective on healthcare expenditure in the last year of life

Authors: S Ranchod, M Abraham and J Bloch

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.
Keywords: Medical schemes, last year of life, decedent costs

An Actuarial perspective on healthcare expenditure in the last year of life

 

Catastrophe modelling: deriving the 1-in-200 year mortality shock for a South African insurer’s capital requirements under Solvency Assessment

Authors: AA Plantinga, DJ Corubolo and RJ Clover

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.
It has been found that a worldwide pandemic is by far the main risk in terms of number of deaths in
a catastrophe and, given that this is the most significant component of catastrophe risk, prior research
on this risk in an South African context is summarised and revisited.

Keywords: Life catastrophe; mortality shock; Solvency II; Solvency Assessment and Management (SAM);
pandemic; stochastic model; 1-in-200

Catastrophe modelling: deriving the 1-in-200 year mortality shock for a South African insurer’s capital requirements under Solvency Assessment


Jump tests for semimartingales

Authors: L Hong and J Zou

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.
Keywords: Asset price; Black–Scholes; equity-linked annuity; variable annuity

Jump tests for semimartingales

 

Reserves in the multi-state health insurance model with stochastic interest of diffusion type

Author: F Adékambi

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.
Keywords: Multi-state life insurance; semi-Markov model; counting process; first conditional moment; partial
differential equations; Markov chain

Reserves in the multi-state health insurance model with stochastic interest of diffusion type

 

Pricing variable annuity guarantees in South Africa under a Variance-Gamma model

Author: AM Ngugi, F Maré and R Kufakunese

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.
Keywords: Embedded derivatives; options; variable annuity; Variance-Gamma; hedging

Pricing variable annuity guarantees in South Africa under a Variance-Gamma model

 

The process of ethical decision-making in South African retirement funds

Author: MBJ Butler, TL Reddy and R da Silva

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.
Keywords: Ethics; ethical framework; retirement fund; trustees; actuaries; fiduciary duties; regulation; theory of
right action; utilitarianism; virtue ethics; ethics of care; theory of common good; theory of justice

The process of ethical decision-making in South African retirement funds


Other articles

Editorial: Writing with impact (pdf)

Emerging Thought: Paul Lewis, Thoughts on professionalism (pdf)

Abstracts of recent postgraduate theses and dissertations at South African universities (pdf)

Abstracts of articles in other South African journals (pdf)

Cumulative index (pdf)