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.
{"title":"Reserves in the multi-state health insurance model with stochastic interest of diffusion type","authors":"Franck Adékambi","doi":"10.4314/SAAJ.V15I0.5","DOIUrl":"https://doi.org/10.4314/SAAJ.V15I0.5","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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-of life 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.
{"title":"An actuarial perspective on healthcare expenditure in the last year of life","authors":"S. Ranchod, J. Bloch, M. Abraham","doi":"10.4314/SAAJ.V15I1.2","DOIUrl":"https://doi.org/10.4314/SAAJ.V15I1.2","url":null,"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-of life 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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
{"title":"A scenario approach to estimate the maximum foreseeable loss for buildings due to an earthquake in Cape Town","authors":"A. Kijko, A. Smit, Natalie Van De Coolwijk","doi":"10.4314/SAAJ.V15I1.1","DOIUrl":"https://doi.org/10.4314/SAAJ.V15I1.1","url":null,"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","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Pricing variable annuity guarantees in South Africa under a Variance-Gamma model","authors":"A. Ngugi, E. Maré, Rodwell Kufakunesu","doi":"10.4314/SAAJ.V15I1.6","DOIUrl":"https://doi.org/10.4314/SAAJ.V15I1.6","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Catastrophe modelling: deriving the 1-in-200 year mortality shock for a South African insurer’s capital requirements under Solvency Assessment and Management","authors":"Adam Plantinga, D. Corubolo, R. Clover","doi":"10.4314/SAAJ.V15I1.3","DOIUrl":"https://doi.org/10.4314/SAAJ.V15I1.3","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Jump tests for semimartingales","authors":"Liang Hong, J. Zou","doi":"10.4314/SAAJ.V15I1.4","DOIUrl":"https://doi.org/10.4314/SAAJ.V15I1.4","url":null,"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.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70613271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to contextualise the gender status of the South African actuarial profession, both historically and relative to elsewhere in the world, as well as to establish the current level of representation of women in the profession. The authors have investigated the extent to which women are represented in different age groups and at various stages of the qualification process. They find that 85% of Fellow members of the Actuarial Society in 2010 are male but that women represent at least 30% of student members and younger cohorts. Given that people enter the profession primarily from undergraduate degrees in actuarial science, the authors have analysed the relative performance of female students enrolling for an Actuarial Science degree at the University of Cape Town. They find that the proportion of entrants who are female has increased over time but that persistency rates for female students are lower than for male students. They identify the need for further research to establish the underlying reasons for the gender differentials in entrants to university programmes and persistency, and conclude that universities, actuarial employers and the profession have a role to play in improving the perception of the profession and the experiences of women in the classroom and workplace.
本文的目的是将南非精算行业的性别地位置于历史和相对于世界其他地方的背景下，并建立目前女性在该行业的代表性水平。作者调查了妇女在不同年龄组和在资格程序的不同阶段所占的比例。他们发现，2010年精算学会会员中有85%是男性，但在学生会员和年轻会员中，女性至少占30%。考虑到人们主要从精算学本科学位进入这个行业，作者分析了开普敦大学(University of Cape Town)攻读精算学学位的女学生的相对表现。他们发现，随着时间的推移，女性新生的比例有所增加，但女学生的坚持率低于男学生。他们认为有必要进行进一步的研究，以确定大学课程和持久性的性别差异的根本原因，并得出结论认为，大学、精算雇主和精算专业在改善妇女在课堂和工作场所对该专业的认识和经验方面可以发挥作用。
{"title":"The gender profile of the South African actuarial profession","authors":"S. Ramjee, Fg Sibiya, K. Dreyer","doi":"10.4314/SAAJ.V13I1.2","DOIUrl":"https://doi.org/10.4314/SAAJ.V13I1.2","url":null,"abstract":"The aim of this paper is to contextualise the gender status of the South African actuarial profession, both historically and relative to elsewhere in the world, as well as to establish the current level of representation of women in the profession. The authors have investigated the extent to which women are represented in different age groups and at various stages of the qualification process. They find that 85% of Fellow members of the Actuarial Society in 2010 are male but that women represent at least 30% of student members and younger cohorts. Given that people enter the profession primarily from undergraduate degrees in actuarial science, the authors have analysed the relative performance of female students enrolling for an Actuarial Science degree at the University of Cape Town. They find that the proportion of entrants who are female has increased over time but that persistency rates for female students are lower than for male students. They identify the need for further research to establish the underlying reasons for the gender differentials in entrants to university programmes and persistency, and conclude that universities, actuarial employers and the profession have a role to play in improving the perception of the profession and the experiences of women in the classroom and workplace.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2013-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70612220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper extends previous work of the authors to reconsider the capital-asset pricing model (CAPM) in South Africa in real terms. As in that work, the main question this study aimed to answer remains: Can the CAPM be accepted in the South African market for the purposes of the stochastic modelling of investment returns in typical actuarial applications? To test the CAPM in real terms, conventional and index-linked bonds were included both in the composition of the market portfolio and in tests of the securities market line. For the investigation, quarterly total returns from the FTSE/JSE all-share index listed on the JSE Securities Exchange from 30 September 1964 to 31 December 2010 were used, together with yields on government bonds and consumer price indices over the same period. As expressed in the securities market line, the CAPM suggests that higher systematic risk, as measured by beta, is associated with higher expected returns, and that the relationship between expected return and beta is linear. In this investigation the above-mentioned predictions of the CAPM were tested for the South African market. Regression tests both of the zero-beta and standard versions of the CAPM were made, using both prior betas and in-period betas. Hotelling's test was also applied, as well as a regression analysis. These tests were made for individual periods as well as for all periods combined.
{"title":"The capital-asset pricing model reconsidered : tests in real terms on a South African market portfolio comprising equities and bonds","authors":"R. Thomson, T. Reddy","doi":"10.4314/SAAJ.V13I1.7","DOIUrl":"https://doi.org/10.4314/SAAJ.V13I1.7","url":null,"abstract":"This paper extends previous work of the authors to reconsider the capital-asset pricing model (CAPM) in South Africa in real terms. As in that work, the main question this study aimed to answer remains: Can the CAPM be accepted in the South African market for the purposes of the stochastic modelling of investment returns in typical actuarial applications? To test the CAPM in real terms, conventional and index-linked bonds were included both in the composition of the market portfolio and in tests of the securities market line. For the investigation, quarterly total returns from the FTSE/JSE all-share index listed on the JSE Securities Exchange from 30 September 1964 to 31 December 2010 were used, together with yields on government bonds and consumer price indices over the same period. As expressed in the securities market line, the CAPM suggests that higher systematic risk, as measured by beta, is associated with higher expected returns, and that the relationship between expected return and beta is linear. In this investigation the above-mentioned predictions of the CAPM were tested for the South African market. Regression tests both of the zero-beta and standard versions of the CAPM were made, using both prior betas and in-period betas. Hotelling's test was also applied, as well as a regression analysis. These tests were made for individual periods as well as for all periods combined.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70612508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the methodology underlying the graduation of the mortality of members of group schemes in South Africa underwritten by life insurance companies under group life-insurance arrangements is described and the results are presented. A multivariate parametric curve was fitted to the data for the working ages 25 to 65 and comparisons are made with the mortality rates from the SA85-90 ultimate rates for insured lives and the ASSA2008 AIDS and demographic model. The results show that the mortality of members of group schemes is lower than that of the general population, mortality decreasing with increasing salary, as would be expected. For males it was found that there were differences in mortality rates by industry for a given salary band, whereas for females these differences only occurred in the lower salary bands. Furthermore, there is evidence of the healthy-worker effect at ages 60 and above, where the mortality rates appear to level off or even decrease as age increases. This contrasts with the mortality rates from the SA85-90 ultimate rates for insured lives and the ASSA2008 AIDS and demographic model, which increase exponentially.
{"title":"Modelling the mortality of members of group schemes in South Africa","authors":"JC Clur, R. Dorrington, K. Schriek, PL Lewis","doi":"10.4314/SAAJ.V13I1.5","DOIUrl":"https://doi.org/10.4314/SAAJ.V13I1.5","url":null,"abstract":"In this paper, the methodology underlying the graduation of the mortality of members of group schemes in South Africa underwritten by life insurance companies under group life-insurance arrangements is described and the results are presented. A multivariate parametric curve was fitted to the data for the working ages 25 to 65 and comparisons are made with the mortality rates from the SA85-90 ultimate rates for insured lives and the ASSA2008 AIDS and demographic model. The results show that the mortality of members of group schemes is lower than that of the general population, mortality decreasing with increasing salary, as would be expected. For males it was found that there were differences in mortality rates by industry for a given salary band, whereas for females these differences only occurred in the lower salary bands. Furthermore, there is evidence of the healthy-worker effect at ages 60 and above, where the mortality rates appear to level off or even decrease as age increases. This contrasts with the mortality rates from the SA85-90 ultimate rates for insured lives and the ASSA2008 AIDS and demographic model, which increase exponentially.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70612319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Individuals in defined-contribution retirement funds currently have a number of options as to how to finance their post-retirement spending. The paper considers the ranking of selected annuitisation strategies by the probability of ruin and by expected discounted utility under different scenarios. 'Ruin' is defined as occurring when income falls below a given threshold, but does not relate to the extent of that deficit. If there is insufficient money to buy an inflation-linked annuity at retirement, then the minimisation of the probability of ruin tends to result in living annuities with a high equity content. This is because the objective function does not reflect the extent of shortfall of income or the investor's level of risk aversion. The authors argue that this is a limitation to using the minimisation of the probability of ruin. Expected discounted utility may be more difficult to apply in practice, because of the complexity of explaining the approach to investors and the need to estimate a greater number of parameters explicitly. The authors argue that the use of expected discounted utility is, however, likely to be more representative of most investors' perception of risk, and illustrate its use by applying an extended discounted utility model that caters for the bequest motive and different reference income levels.
{"title":"A COMPARISON OF PROBABILITY OF RUIN AND EXPECTED DISCOUNTED UTILITY AS OBJECTIVE FUNCTIONS FOR CHOOSING A POST-RETIREMENT INVESTMENT STRATEGY","authors":"M. Butler, B. Hu, D. Kloppers","doi":"10.4314/SAAJ.V13I1.6","DOIUrl":"https://doi.org/10.4314/SAAJ.V13I1.6","url":null,"abstract":"Individuals in defined-contribution retirement funds currently have a number of options as to how to finance their post-retirement spending. The paper considers the ranking of selected annuitisation strategies by the probability of ruin and by expected discounted utility under different scenarios. 'Ruin' is defined as occurring when income falls below a given threshold, but does not relate to the extent of that deficit. If there is insufficient money to buy an inflation-linked annuity at retirement, then the minimisation of the probability of ruin tends to result in living annuities with a high equity content. This is because the objective function does not reflect the extent of shortfall of income or the investor's level of risk aversion. The authors argue that this is a limitation to using the minimisation of the probability of ruin. Expected discounted utility may be more difficult to apply in practice, because of the complexity of explaining the approach to investors and the need to estimate a greater number of parameters explicitly. The authors argue that the use of expected discounted utility is, however, likely to be more representative of most investors' perception of risk, and illustrate its use by applying an extended discounted utility model that caters for the bequest motive and different reference income levels.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70612457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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