- Email: [email protected]
233013 (E10, E11) The principle of equivalence revisited
Abstracts and Reviews the premium rate depends on u in such way that the safety loading decreases to zero as u -~o.
Keywords: Probability of Ruin.
303
revenues from insurance industry. The study raises concerns about the potential for a systematic disruption of the supply of reinsurance in the international marketplace.
Keywords: Lloyd's insurance, Reinsurance, Financial distress, Contagion M31: E X P E R I E N C E RATING, C R E D I B I L I T Y T H E O R Y , BONUS-MALUS SYSTEMS
M52: REINSURANCE, RETENTIONS 233010 (M31, M10)
Risk-Adjusted Credibility Premiums Using Distorted Probabilities Wang S.S., Young V.R., Scandinavian Actuarial Journal, 1998, No.2 Denneberg (1990) and Wang (1996a) propose that one calculate risk-adjusted insurance premiums as the expectation with respect to a distorted probability measure, a non-additive set function. This premium principle is supported by the theories of decision making of Yaari (1987) and of Schmeidler (1989). Denneberg (1994a) presents three conditioning rules for updating non-additive set functions in light of available information. In this work, the authors show how to apply these three update rules to calculate a risk-adjusted credibility premium and, thereby, combine credibility theory with this relatively new premium principle. The main result is that, for some pairs of distortion function and update rule, one gets the same risk-adjusted credibility premium by distorting the predictive probability distribution, as required by the theory of Yaari, or by updating the distorted probability, as required by the theory of Schmeidler.
233012 (M52)
Optimal Proportional Reinsurance Policies for Diffusion Models Hojgaard B., Taksar M., Scandinavian Actuarial Journal, 1998, No.2 q~ When applying a proportional reinsurance policy the reserve of the insurance company {R,=} is governed by a SDE dR,= = a~(t)~tdt + a=(t)odW, where {W,} is a standard Brownian motion, p,, o > 0 are constants and 0 <_a=(t) _< 1 is the control process, where l - a~,(t) denotes the fraction that is reinsured at time t. The aim of the paper is to find a policy that maximizes the return function ¢'~(x)= E ( ~e-"RFdt, where c > 0, z= is the time ,sO of ruin and x refers to the initial reserve.
Keywords: Dif/itsion models, Stochastic control, HJB equation.
E: INSURANCE ECONOMICS
EIO: INSURANCE RELATED M A T H E M A T I C A L ECONOMICS,GENERAL AND MISCELLANEOUS
Keywords: Credibility, Premium calculation principle, Choquet integral, Non-addictive measure.
233013 (El0, E11)
M51: RISK SHARING ARRANGEMENTS
The Principle of Equivalence Revisited Persson S.A., Scandinavian Actuarial Journal, 1998. No. 2
233011 (M51, M52)
Lloyd's Financial Distress and Contagion within the US Property and Liability Insurance Industry Fields J.A., Klein L.S., Myskowski E.G., Journal of Risk and Uncertainty, Volume 16, No 2, May~June 1998 The intra-industry effect of Lloyd's financial distress on publicly traded US insurance companies is examined. Given Lloyd's prominence in the international insurance industry, large losses raised questions about the industry's capacity for certain types of risks and the financial solvency of other insurers. The market value of US property-liability insurers fell significantly at the announcement. This decline is related to the firm's
Based on financial theory, a valuation model --including stochastic interest rates--for traditional life insurance contracts is derived. The interpretation of the principle of equivalence may be revisited in this framework; single premiums are found as expected present values under a risk adjusted probability measure. Using a specific model of the term structure some new formulas for the market value of various life insurance contracts are derived. A partial differential equation for the market values of the assurances is deduced, corresponding to the traditional Thiele's differential equation of classical actuarial science. This equation contains some interesting new terms.
Keywords: Thiele's d!fferential equation. Principle q["
304
Abstracts and Reviews
equivalence, Financial risk, Arbitrage pricing theory, Stochastic interest rate. 233014 (El 0) The Dividend Problem in a Diffusive Stochastic Model di Lorenzo E., Sibillo M., Deutsche Gesellschafi Fiir
Versicherungsmathematik, Band XX111, Heft 4, October 1998. The expectation of the discounted dividend payments is determined in the framework of a mathematical model in which financial risk is considered. In particular, starting from a diffusive stochastic model for the cash-balance, the expression of the expectation of the discounted dividends is obtained as the solution of a differential equation, with appropriate boundary conditions relating to the presence of a barrier regulating dividend payments.
Keywords." Financial Risk, Stochastic model. 233015 (El0) The Rate of Index Participation as a Distinguishing Feature of Guaranteed Equity-Linked Life Insurance Policies Russ J., Schittenhelm F.A., Deutsche Gesellschaft Fiir
Versicherungsmathematik, Band XX111, Heft 4, October 1998. The authors define a rich class of possible payoff patterns for guaranteed equity-linked life insurance contracts. They show how the fair rate of index participation can be calculated within a model for the economy where the short rate is deterministic. For a great variety of 42 different products --including several averaging variants-- they calculate the participation rate under different market scenarios and discuss the dependency of the rate of index participation on the product design in great detail. Furthermore, the authors show how the products offered in Germany fit into our class of products.
Keywords: Life insurance, Linked policies. 233016 (El0, B13) Valuation of pensions with pre-scheduled payment dates Jensen G., Deutsche Gesellschaft Fiir Versicherungs-
mathematik, Band XXlll, Heft 4, October 1998. The paper presents an algorithm with which, on the basis of a modification suggested by Neuburger, the present values of pensions can be calculated in a uniform manner. The procedure does not change if the biometrical probabilities and the interest rate are time-dependent.
Moreover, the profiles of the pensions can be arbitrary and time-dependent too. The algorithm supplies simultaneously all simple and composed present values which are necessary in balancing. Additionally, the realization with Excel is outlined.
Keywords: Pension, Present value. 233017 (El0) Consumer Capital Market Constraints and Guaranteed Renewable Insurance Frick K., Journal of Risk and Uncertainty, Volume 16.
No 3, July~August 1998 A market is analyzed in which individuals can purchase guaranteed renewable insurance policies to insure against the risk of loss in the current period and the risk of increased probability of loss. Individuals who cannot borrow will purchase partially guaranteed renewable insurance at most. Relatively impatient individuals may purchase policies with no guaranteed renewability features. Without borrowing, the results are similar regardless of whether consumers can save.
Keywords: Insurance, renewability, Capital market constraints, Subjective rate of time preference. 233018 (El0) Time Insensitivity for Protective Investments Kunreuther H., Onculer A., Slovic P., Journal of Risk
and Uncertainty, ~blume 16, No 3, July~August 1998 Investment in protective measures involve an initial immediate cost in exchange for a stream of potential benefits accruing over time in the form of reduced expected losses. This paper describes two studies in which individuals were asked both to make choices and indicate the maximum amount they were willing to pay (WTP) for such protective measures. By varying the number of years that the measures provided protection, the authors observed four different decision strategies that individuals use to determine their maximum WTP. The findings from these experiments strongly suggest that most individuals do not take into account the added benefits of having a protective measure in place over a long period of time when determining the likelihood of purchasing protection or the maximum price they are willing to pay. The behavior of a relatively small proportion of the subjects was consistent with a discounted utility model. Most subjects were either myopic in their behavior or did not change their maximum WTP as the time horizon changed. Despite the fact that most subjects were insensitive to time changes, they were generally willing to purchase the protective
Keywords: Probability of Ruin.
303
revenues from insurance industry. The study raises concerns about the potential for a systematic disruption of the supply of reinsurance in the international marketplace.
Keywords: Lloyd's insurance, Reinsurance, Financial distress, Contagion M31: E X P E R I E N C E RATING, C R E D I B I L I T Y T H E O R Y , BONUS-MALUS SYSTEMS
M52: REINSURANCE, RETENTIONS 233010 (M31, M10)
Risk-Adjusted Credibility Premiums Using Distorted Probabilities Wang S.S., Young V.R., Scandinavian Actuarial Journal, 1998, No.2 Denneberg (1990) and Wang (1996a) propose that one calculate risk-adjusted insurance premiums as the expectation with respect to a distorted probability measure, a non-additive set function. This premium principle is supported by the theories of decision making of Yaari (1987) and of Schmeidler (1989). Denneberg (1994a) presents three conditioning rules for updating non-additive set functions in light of available information. In this work, the authors show how to apply these three update rules to calculate a risk-adjusted credibility premium and, thereby, combine credibility theory with this relatively new premium principle. The main result is that, for some pairs of distortion function and update rule, one gets the same risk-adjusted credibility premium by distorting the predictive probability distribution, as required by the theory of Yaari, or by updating the distorted probability, as required by the theory of Schmeidler.
233012 (M52)
Optimal Proportional Reinsurance Policies for Diffusion Models Hojgaard B., Taksar M., Scandinavian Actuarial Journal, 1998, No.2 q~ When applying a proportional reinsurance policy the reserve of the insurance company {R,=} is governed by a SDE dR,= = a~(t)~tdt + a=(t)odW, where {W,} is a standard Brownian motion, p,, o > 0 are constants and 0 <_a=(t) _< 1 is the control process, where l - a~,(t) denotes the fraction that is reinsured at time t. The aim of the paper is to find a policy that maximizes the return function ¢'~(x)= E ( ~e-"RFdt, where c > 0, z= is the time ,sO of ruin and x refers to the initial reserve.
Keywords: Dif/itsion models, Stochastic control, HJB equation.
E: INSURANCE ECONOMICS
EIO: INSURANCE RELATED M A T H E M A T I C A L ECONOMICS,GENERAL AND MISCELLANEOUS
Keywords: Credibility, Premium calculation principle, Choquet integral, Non-addictive measure.
233013 (El0, E11)
M51: RISK SHARING ARRANGEMENTS
The Principle of Equivalence Revisited Persson S.A., Scandinavian Actuarial Journal, 1998. No. 2
233011 (M51, M52)
Lloyd's Financial Distress and Contagion within the US Property and Liability Insurance Industry Fields J.A., Klein L.S., Myskowski E.G., Journal of Risk and Uncertainty, Volume 16, No 2, May~June 1998 The intra-industry effect of Lloyd's financial distress on publicly traded US insurance companies is examined. Given Lloyd's prominence in the international insurance industry, large losses raised questions about the industry's capacity for certain types of risks and the financial solvency of other insurers. The market value of US property-liability insurers fell significantly at the announcement. This decline is related to the firm's
Based on financial theory, a valuation model --including stochastic interest rates--for traditional life insurance contracts is derived. The interpretation of the principle of equivalence may be revisited in this framework; single premiums are found as expected present values under a risk adjusted probability measure. Using a specific model of the term structure some new formulas for the market value of various life insurance contracts are derived. A partial differential equation for the market values of the assurances is deduced, corresponding to the traditional Thiele's differential equation of classical actuarial science. This equation contains some interesting new terms.
Keywords: Thiele's d!fferential equation. Principle q["
304
Abstracts and Reviews
equivalence, Financial risk, Arbitrage pricing theory, Stochastic interest rate. 233014 (El 0) The Dividend Problem in a Diffusive Stochastic Model di Lorenzo E., Sibillo M., Deutsche Gesellschafi Fiir
Versicherungsmathematik, Band XX111, Heft 4, October 1998. The expectation of the discounted dividend payments is determined in the framework of a mathematical model in which financial risk is considered. In particular, starting from a diffusive stochastic model for the cash-balance, the expression of the expectation of the discounted dividends is obtained as the solution of a differential equation, with appropriate boundary conditions relating to the presence of a barrier regulating dividend payments.
Keywords." Financial Risk, Stochastic model. 233015 (El0) The Rate of Index Participation as a Distinguishing Feature of Guaranteed Equity-Linked Life Insurance Policies Russ J., Schittenhelm F.A., Deutsche Gesellschaft Fiir
Versicherungsmathematik, Band XX111, Heft 4, October 1998. The authors define a rich class of possible payoff patterns for guaranteed equity-linked life insurance contracts. They show how the fair rate of index participation can be calculated within a model for the economy where the short rate is deterministic. For a great variety of 42 different products --including several averaging variants-- they calculate the participation rate under different market scenarios and discuss the dependency of the rate of index participation on the product design in great detail. Furthermore, the authors show how the products offered in Germany fit into our class of products.
Keywords: Life insurance, Linked policies. 233016 (El0, B13) Valuation of pensions with pre-scheduled payment dates Jensen G., Deutsche Gesellschaft Fiir Versicherungs-
mathematik, Band XXlll, Heft 4, October 1998. The paper presents an algorithm with which, on the basis of a modification suggested by Neuburger, the present values of pensions can be calculated in a uniform manner. The procedure does not change if the biometrical probabilities and the interest rate are time-dependent.
Moreover, the profiles of the pensions can be arbitrary and time-dependent too. The algorithm supplies simultaneously all simple and composed present values which are necessary in balancing. Additionally, the realization with Excel is outlined.
Keywords: Pension, Present value. 233017 (El0) Consumer Capital Market Constraints and Guaranteed Renewable Insurance Frick K., Journal of Risk and Uncertainty, Volume 16.
No 3, July~August 1998 A market is analyzed in which individuals can purchase guaranteed renewable insurance policies to insure against the risk of loss in the current period and the risk of increased probability of loss. Individuals who cannot borrow will purchase partially guaranteed renewable insurance at most. Relatively impatient individuals may purchase policies with no guaranteed renewability features. Without borrowing, the results are similar regardless of whether consumers can save.
Keywords: Insurance, renewability, Capital market constraints, Subjective rate of time preference. 233018 (El0) Time Insensitivity for Protective Investments Kunreuther H., Onculer A., Slovic P., Journal of Risk
and Uncertainty, ~blume 16, No 3, July~August 1998 Investment in protective measures involve an initial immediate cost in exchange for a stream of potential benefits accruing over time in the form of reduced expected losses. This paper describes two studies in which individuals were asked both to make choices and indicate the maximum amount they were willing to pay (WTP) for such protective measures. By varying the number of years that the measures provided protection, the authors observed four different decision strategies that individuals use to determine their maximum WTP. The findings from these experiments strongly suggest that most individuals do not take into account the added benefits of having a protective measure in place over a long period of time when determining the likelihood of purchasing protection or the maximum price they are willing to pay. The behavior of a relatively small proportion of the subjects was consistent with a discounted utility model. Most subjects were either myopic in their behavior or did not change their maximum WTP as the time horizon changed. Despite the fact that most subjects were insensitive to time changes, they were generally willing to purchase the protective