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071040 (E10, E11) The preservation of multivariate comparative statics in nonexpected utility theory
174
Abstracts and Reviews
surplus and its linkage to liabilities over time is explained, and the concept of a calendar period balance sheet as the sum of underlying accident period balance sheets is introduced. Measures of rates of return on surplus inherent in internal rate of return and net present value discounted cash flow models are explained, and the conditions under which the returns are equivalent are demonstrated. This paper also presents a methodology for determining a bench mark amount of surplus needed to support writings in a line of business in order to control the probability of insolvency. The methodology is based on a consideration of both the magnitude and the variability in underwriting, underwriting cash flows, and interest rates. (Author) Keywords" Surplus, Rate of Return.
stop-loss premium should be to be able to pay the expected value of the first claim. Some very simple examples are given as illustration. (Author) Keywords: Stop-Loss.
E10: INSURANCE RELATED M A T H E M A T I C A L ECONOMICS,GENERALAND MISCELLANEOUS
071040 (El0, E l i ) The preservation of multivariate comparative statics in nonexpected utility theory. Schlee E.E., Arizona State University, Journal of Risk and Uncertainty, Vol. 9, 1994, pp. 257-272.
In the paper retention is defined as part of an insurance that deducts claims. The paper treats where and how retention is applied. Several aspects in which retention has a function, such as prevention, claims behaviour, moral risk, selection and costs are described. The reduction of the risk premium caused by a retention is demonstrated by a simple and clear example. (Author) Keywords: Retention.
This article investigates the preservation of multivariate expected utility comparative statics for "smooth" nonexpected utility representations. Specifically, the author answers the following question: if an expected utility comparative statics property depends only on preferences over sure prospects, then when will a nonexpected utility maximizer with identical sure preferences also satisfy that property? The author demonstrates that the effects of increased risk aversion are preserved under the "Almost Degenerate Independence" axiom, but that those of distribution changes of exogenous risks are not preserved under stringent assumptions. Hence, nonexpected utility comparative statics may diverge from expected utility, even for "first-order" properties - those whose effect is determinable from restrictions on "local" utility functions. (Author) Keywords: Expected Utility, Nonexpected Utility, Risk Aversion, Comparative Statics, Multivariate Risk.
O71039 (M52) Stop 'Stop-loss' Loss. Kling B.M., Heterogeniteit in Verzekering Amicorum G.W. de Wit, 1994.
071041 (El0) Rate of return - policyholder, company, and shareholder perspectives. Bingham R.E., Proceedings Casualty Actuarial Society, Vol. LXXX,, hr. 152, 1993, pp. 110-147.
M52: REINSURANCE, RETENTIONS
071038 (M52) Retention. Baaij J.G., University of Amsterdam, Heterogeniteit in Verzekering - Liber Amicorum G. W. de Wit, 1994.
Liber
Stop-loss contracts with high retentions have low probabilities on claim payments. Given the occurrence of a claim, however, the conditional expected value exceeds the stop-loss premium. For large portfolios of stop-loss contracts, there is no real difference with other type of insurances. But for a single stop-loss contract or a very small portfolio of stop-loss contracts, the law of large numbers can no longer be applied. In that case the author investigates how large the reserve in terms of the
This paper discusses rate of return from the policyholder, company, and shareholder perspectives. Both net present value (NPV) and internal rate of return (IRR) variations of discounted cash flow models are used to demonstrate two important considerations: The relationship between policyholder liabilities and surplus, and the release of income and return of surplus to the shareholder. A method for determining the "insurance
Abstracts and Reviews
surplus and its linkage to liabilities over time is explained, and the concept of a calendar period balance sheet as the sum of underlying accident period balance sheets is introduced. Measures of rates of return on surplus inherent in internal rate of return and net present value discounted cash flow models are explained, and the conditions under which the returns are equivalent are demonstrated. This paper also presents a methodology for determining a bench mark amount of surplus needed to support writings in a line of business in order to control the probability of insolvency. The methodology is based on a consideration of both the magnitude and the variability in underwriting, underwriting cash flows, and interest rates. (Author) Keywords" Surplus, Rate of Return.
stop-loss premium should be to be able to pay the expected value of the first claim. Some very simple examples are given as illustration. (Author) Keywords: Stop-Loss.
E10: INSURANCE RELATED M A T H E M A T I C A L ECONOMICS,GENERALAND MISCELLANEOUS
071040 (El0, E l i ) The preservation of multivariate comparative statics in nonexpected utility theory. Schlee E.E., Arizona State University, Journal of Risk and Uncertainty, Vol. 9, 1994, pp. 257-272.
In the paper retention is defined as part of an insurance that deducts claims. The paper treats where and how retention is applied. Several aspects in which retention has a function, such as prevention, claims behaviour, moral risk, selection and costs are described. The reduction of the risk premium caused by a retention is demonstrated by a simple and clear example. (Author) Keywords: Retention.
This article investigates the preservation of multivariate expected utility comparative statics for "smooth" nonexpected utility representations. Specifically, the author answers the following question: if an expected utility comparative statics property depends only on preferences over sure prospects, then when will a nonexpected utility maximizer with identical sure preferences also satisfy that property? The author demonstrates that the effects of increased risk aversion are preserved under the "Almost Degenerate Independence" axiom, but that those of distribution changes of exogenous risks are not preserved under stringent assumptions. Hence, nonexpected utility comparative statics may diverge from expected utility, even for "first-order" properties - those whose effect is determinable from restrictions on "local" utility functions. (Author) Keywords: Expected Utility, Nonexpected Utility, Risk Aversion, Comparative Statics, Multivariate Risk.
O71039 (M52) Stop 'Stop-loss' Loss. Kling B.M., Heterogeniteit in Verzekering Amicorum G.W. de Wit, 1994.
071041 (El0) Rate of return - policyholder, company, and shareholder perspectives. Bingham R.E., Proceedings Casualty Actuarial Society, Vol. LXXX,, hr. 152, 1993, pp. 110-147.
M52: REINSURANCE, RETENTIONS
071038 (M52) Retention. Baaij J.G., University of Amsterdam, Heterogeniteit in Verzekering - Liber Amicorum G. W. de Wit, 1994.
Liber
Stop-loss contracts with high retentions have low probabilities on claim payments. Given the occurrence of a claim, however, the conditional expected value exceeds the stop-loss premium. For large portfolios of stop-loss contracts, there is no real difference with other type of insurances. But for a single stop-loss contract or a very small portfolio of stop-loss contracts, the law of large numbers can no longer be applied. In that case the author investigates how large the reserve in terms of the
This paper discusses rate of return from the policyholder, company, and shareholder perspectives. Both net present value (NPV) and internal rate of return (IRR) variations of discounted cash flow models are used to demonstrate two important considerations: The relationship between policyholder liabilities and surplus, and the release of income and return of surplus to the shareholder. A method for determining the "insurance