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081034 (M12, B13) Moving average rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme
Abstracts and Reviews M l l : STOCHASTIC MODELS FOR CLAIMS FREQUENCY, CLAIM SIZE AND AGGREGATE CLAIMS
081031 ( M l l , M13) Stochastic Calculus in Actuarial Science. Norberg R., University of Copenhagen, Copenhagen,
Laboratory of Actuarial Mathematics, University of Copenhagen, Working Paper No. 135, 1995. The present paper addresses a class of problems in insurance mathematics that all amount to determining the conditional expected value of some functional of some stochastic process. It demonstrates by examples how modern stochastic calculus opens for extensions of existing results to models of greater complexity and, hence, closer resemblance to various real life situations and also represents methodological unification. The same set of tools are used to determine seemingly unrelated entities from traditionally segregated subfields of actuarial mathematics, including first and higher order moments of present values in life insurance, total claims distributions in non-life insurance, and the probability of ruin in actuarial risk theory.
Keywords: stochastic probability of ruin.
calculus,
present
values,
MI2: MODELLING OF PORTFOLIOS AND COLLECTIVES
081032 (M12) Perception and Acceptance of Technological and Environmental Risks: Why are Poor Countries less concerned? Sokolowska J., Tyszka T., Institute of Psychology, Polish Academy of Sciences, Warsaw, Risk Analysis,
Vol. 15, Number 6, 1995, pp. 733-743. The research has been aimed at answering two questions: (1) what factors impact perception and acceptance of technological and environmental hazards?, (2) why are rich societies involved more in protecting their environment and health than poor societies? Data has been collected from representative samples of two countries - Poland and Sweden. The results indicate that (1) country to earlier findings, the inverse relations between perceived benefits and dangers of hazards has not been observed, (2) acceptance of a risk has been mostly influenced by perceived benefits, (3) rejection of a risk has been mostly influenced by its perceived harmful consequences. Concerning the second question,
141
it has been found that (1) perceived hazard's danger and benefit is not the only factor that impacts its acceptance, and (2) a broader economic context can impact acceptance (tolerance) of hazards. It has been found that being aware of high dangers and not very high benefits of hazardous activities, Poles still have accepted them. Thus, Poles seem to follow an old proverb: "When one does not have what one likes, one has to like what one has".
Keywords: risk perception, risk acceptance, environmental risks, cross-cultural comparison. 081033 (M12, B20) DO Poor People have a Stronger Relationship between Income and Mortality than the Rich? Implications of Panel Data for Health-Health Analysis. Chapman K.S., Hariharan D., California State University at Northridge, Northridge, State University of New York at Buffalo, Journal Risk and Uncertainty,
Volume 12, Number 1, 1996, pp. 51-63. Articles developing health-health analysis have used the observation that richer people tend to face reduced mortality risk to estimate the break-even cost per life saved of health regulations. If government requires that the private sector spend more than this break-even cutoff, the risk of dying due to reduced health investment is increased by more than it will be reduced by the direct action of the health regulation. We use panel data to suggest that the relationship between income and the probability of death is greater for poor people than for the rich. As a consequence, break-even cutoffs are roughly twice as large for the richest 20% of the population than they are for the poorest 20%. The nonlinearity in the income-to-mortality linkage also implies that income transfers between income groups which are ignored in traditional cost-benefit analysis will affect the conclusions of health-health analysis significantly.
Keywords: health-health analysis, health economics, safety regulation, value of life. 081034 (MI2, B13) Moving Average Rates of Return and the Variability of Pension Contributions and Fund Levels for a Defined Benefit Pension Scheme. Haberman S., Wong L.Y.P., Department of Actuarial Science and Statistics, City University, London, City
University, Actuarial Research Paper No. 88, 1996. A mathematical model is described which
142
Abstracts and Reviews
facilitates the comparison of different pension funding methods for a defined benefit pension scheme. Real investment rates of return to the pension fund are assumed to be represented by a moving average model for the corresponding force of interest. Expressions for the moments of the contribution rate and fund level are then derived. This leads to a discussion of methods of funding which are optimal in the sense of choosing the period for spreading surpluses and deficiencies in order to reduce the variability of both contributions and fund levels. The results are compared with those obtained when the investment returns are lid or autoregressive and, in this sense, the paper is a natural successor to Haberman (1994).
Keywords: pension funding, moving average rates of return, optimal spread period, variability of contributions and fund.
M21: GRADUATION 081035 (M21) Whittaker Graduation and Parametric State Space Models. Verrall R.J., Department of Actuarial Science and Statistics, City University, London, City University,
Actuarial Research Paper No. 79, 1995. This paper considers the extension of parametric graduation to dynamic state space between models. It is shown that Whittaker graduation can be written as one particular dynamic state space model, and can therefore be connected to parametric graduation. The framework of generalised linear models is used, and Whittaker graduation is performed using a dynamic generalised linear model rather than the usual normal approximation to the (generalised) likelihood. The main purpose of this paper is to show how a whole further class of flexible models can be included within the same framework as parametric graduation. It is a paper which both unifies and extends existing graduation theory.
Keywords." generalised linear models, graduation, state space models. M31: EXPERIENCE RATING, CREDIBILITY THEORY, BONUS-MALUS SYSTEMS 081036 (M31) A Note on D-Optimal Designs for a Logistic Regression Model. Sebastiani P., Settimi R., Department of Actuarial
Science and Statistics, City University, London, City
University, Statistical Research Paper No. 4, 1996. We prove that a 2 point design suggested by Ford, Torsney and Wu (1992) for a simple logistic regression model is D-optimal. We also propose designs which give efficient alternatives to the D-optimal designs and require less information on the parameters.
Keywords: D-optimality, efficiency, logistic regression.
M42: LOSS RESERVES (INCLUDING I.B.N.R.) 081037 (M42) Claims Reserving and Generalised Additive Models. Verrall R.J., Department of Actuarial Science and Statistics, City University, London, City University,
Actuarial Research Paper No. 80, 1995. This paper shows how non-parametric smoothing can be applied in the context of claims reserving. The paper concentrates on the chain-ladder technique, within the framework of the chain-ladder linear model, but the methods can easily be applied to other models. It is shown that non-parametric smoothing can provide more stable reserve estimates, and is an alternative to other methods suggested for this purpose such as the Kalman filter. The methods are implemented in the statistical package S-PLUS.
Keywords: chain-ladder technique, claims reserving, generalised additive models, generalised linear models, non-parametric smoothing. 081038 (M42) An Extension of Mack's Model for the Chain Ladder Method. Schmidt K.D., Schnaus A., Institut fiir Mathematische Stochastik, Technische Universit~it Dresden, Dresden,
Institutfur MathematischeStochastik, Dresdner Schriften zur Versicherungsmathematik, 4, 1995. The chain ladder method is a simple and suggestive tool in claims reserving, and various attempts have been made aiming at its justification in a stochastic model. Remarkable progress has been achieved by Mack and Schnieper who considered models with assumptions on conditional distributions. This paper extends Mack's model and proposes a basic model in a decision theoretic setting. The model allows to characterize optimality of the chain ladder at the end of the first nonobservable development and for aggregate claims at the end of the first non-observable calendar year.
Keywords: IBNR, chain ladder method, model of Mack.
081031 ( M l l , M13) Stochastic Calculus in Actuarial Science. Norberg R., University of Copenhagen, Copenhagen,
Laboratory of Actuarial Mathematics, University of Copenhagen, Working Paper No. 135, 1995. The present paper addresses a class of problems in insurance mathematics that all amount to determining the conditional expected value of some functional of some stochastic process. It demonstrates by examples how modern stochastic calculus opens for extensions of existing results to models of greater complexity and, hence, closer resemblance to various real life situations and also represents methodological unification. The same set of tools are used to determine seemingly unrelated entities from traditionally segregated subfields of actuarial mathematics, including first and higher order moments of present values in life insurance, total claims distributions in non-life insurance, and the probability of ruin in actuarial risk theory.
Keywords: stochastic probability of ruin.
calculus,
present
values,
MI2: MODELLING OF PORTFOLIOS AND COLLECTIVES
081032 (M12) Perception and Acceptance of Technological and Environmental Risks: Why are Poor Countries less concerned? Sokolowska J., Tyszka T., Institute of Psychology, Polish Academy of Sciences, Warsaw, Risk Analysis,
Vol. 15, Number 6, 1995, pp. 733-743. The research has been aimed at answering two questions: (1) what factors impact perception and acceptance of technological and environmental hazards?, (2) why are rich societies involved more in protecting their environment and health than poor societies? Data has been collected from representative samples of two countries - Poland and Sweden. The results indicate that (1) country to earlier findings, the inverse relations between perceived benefits and dangers of hazards has not been observed, (2) acceptance of a risk has been mostly influenced by perceived benefits, (3) rejection of a risk has been mostly influenced by its perceived harmful consequences. Concerning the second question,
141
it has been found that (1) perceived hazard's danger and benefit is not the only factor that impacts its acceptance, and (2) a broader economic context can impact acceptance (tolerance) of hazards. It has been found that being aware of high dangers and not very high benefits of hazardous activities, Poles still have accepted them. Thus, Poles seem to follow an old proverb: "When one does not have what one likes, one has to like what one has".
Keywords: risk perception, risk acceptance, environmental risks, cross-cultural comparison. 081033 (M12, B20) DO Poor People have a Stronger Relationship between Income and Mortality than the Rich? Implications of Panel Data for Health-Health Analysis. Chapman K.S., Hariharan D., California State University at Northridge, Northridge, State University of New York at Buffalo, Journal Risk and Uncertainty,
Volume 12, Number 1, 1996, pp. 51-63. Articles developing health-health analysis have used the observation that richer people tend to face reduced mortality risk to estimate the break-even cost per life saved of health regulations. If government requires that the private sector spend more than this break-even cutoff, the risk of dying due to reduced health investment is increased by more than it will be reduced by the direct action of the health regulation. We use panel data to suggest that the relationship between income and the probability of death is greater for poor people than for the rich. As a consequence, break-even cutoffs are roughly twice as large for the richest 20% of the population than they are for the poorest 20%. The nonlinearity in the income-to-mortality linkage also implies that income transfers between income groups which are ignored in traditional cost-benefit analysis will affect the conclusions of health-health analysis significantly.
Keywords: health-health analysis, health economics, safety regulation, value of life. 081034 (MI2, B13) Moving Average Rates of Return and the Variability of Pension Contributions and Fund Levels for a Defined Benefit Pension Scheme. Haberman S., Wong L.Y.P., Department of Actuarial Science and Statistics, City University, London, City
University, Actuarial Research Paper No. 88, 1996. A mathematical model is described which
142
Abstracts and Reviews
facilitates the comparison of different pension funding methods for a defined benefit pension scheme. Real investment rates of return to the pension fund are assumed to be represented by a moving average model for the corresponding force of interest. Expressions for the moments of the contribution rate and fund level are then derived. This leads to a discussion of methods of funding which are optimal in the sense of choosing the period for spreading surpluses and deficiencies in order to reduce the variability of both contributions and fund levels. The results are compared with those obtained when the investment returns are lid or autoregressive and, in this sense, the paper is a natural successor to Haberman (1994).
Keywords: pension funding, moving average rates of return, optimal spread period, variability of contributions and fund.
M21: GRADUATION 081035 (M21) Whittaker Graduation and Parametric State Space Models. Verrall R.J., Department of Actuarial Science and Statistics, City University, London, City University,
Actuarial Research Paper No. 79, 1995. This paper considers the extension of parametric graduation to dynamic state space between models. It is shown that Whittaker graduation can be written as one particular dynamic state space model, and can therefore be connected to parametric graduation. The framework of generalised linear models is used, and Whittaker graduation is performed using a dynamic generalised linear model rather than the usual normal approximation to the (generalised) likelihood. The main purpose of this paper is to show how a whole further class of flexible models can be included within the same framework as parametric graduation. It is a paper which both unifies and extends existing graduation theory.
Keywords." generalised linear models, graduation, state space models. M31: EXPERIENCE RATING, CREDIBILITY THEORY, BONUS-MALUS SYSTEMS 081036 (M31) A Note on D-Optimal Designs for a Logistic Regression Model. Sebastiani P., Settimi R., Department of Actuarial
Science and Statistics, City University, London, City
University, Statistical Research Paper No. 4, 1996. We prove that a 2 point design suggested by Ford, Torsney and Wu (1992) for a simple logistic regression model is D-optimal. We also propose designs which give efficient alternatives to the D-optimal designs and require less information on the parameters.
Keywords: D-optimality, efficiency, logistic regression.
M42: LOSS RESERVES (INCLUDING I.B.N.R.) 081037 (M42) Claims Reserving and Generalised Additive Models. Verrall R.J., Department of Actuarial Science and Statistics, City University, London, City University,
Actuarial Research Paper No. 80, 1995. This paper shows how non-parametric smoothing can be applied in the context of claims reserving. The paper concentrates on the chain-ladder technique, within the framework of the chain-ladder linear model, but the methods can easily be applied to other models. It is shown that non-parametric smoothing can provide more stable reserve estimates, and is an alternative to other methods suggested for this purpose such as the Kalman filter. The methods are implemented in the statistical package S-PLUS.
Keywords: chain-ladder technique, claims reserving, generalised additive models, generalised linear models, non-parametric smoothing. 081038 (M42) An Extension of Mack's Model for the Chain Ladder Method. Schmidt K.D., Schnaus A., Institut fiir Mathematische Stochastik, Technische Universit~it Dresden, Dresden,
Institutfur MathematischeStochastik, Dresdner Schriften zur Versicherungsmathematik, 4, 1995. The chain ladder method is a simple and suggestive tool in claims reserving, and various attempts have been made aiming at its justification in a stochastic model. Remarkable progress has been achieved by Mack and Schnieper who considered models with assumptions on conditional distributions. This paper extends Mack's model and proposes a basic model in a decision theoretic setting. The model allows to characterize optimality of the chain ladder at the end of the first nonobservable development and for aggregate claims at the end of the first non-observable calendar year.
Keywords: IBNR, chain ladder method, model of Mack.