Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T22:58:55.004Z Has data issue: false hasContentIssue false

Managing uncertainty in a general insurance company

Published online by Cambridge University Press:  20 April 2012

Abstract

A cash flow model is proposed as a way of analysing uncertainty in the future development of a general insurance company. The company is modelled alongside the market in aggregate so that the impact of changes in premium rates relative to the market can be assessed. An extensive computer model is developed along these lines, intended for use in practical applications by actuaries advising the management of genera1 insurance companies. Simulation methods are used to explore the consequences of uncertainty, particularly in regard to inflation and investments. Some comments are made on the role of actuaries in general insurance. Alternative approaches to describing the behaviour of an insurance firm in the market are considered.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, J. C. H. (1959). Gross premium calculation and profit measurement for non-participating insurance. Transactions of the Society of Actuaries, 1959, 4.Google Scholar
Arthur, T. G. & Randall, P. A. (1990). Actuaries, pension funds and investment. J.I.A. 117, 1.Google Scholar
Balzer, L. A. & Benjamin, S. (1980). Dynamic response of insurance systems with delayed profit/loss sharing feedback to isolated unpredicted claims. J.I.A. 107, 513–28.Google Scholar
Balzer, L. A. (1982). Control of insurance systems with delayed profit/loss sharing feedback and persisting unpredicted claims. J.I.A. 109, 285316.Google Scholar
Beard, R. E., Pentikäinen, T. & Pesonen, E. (1984). Risk Theory (3rd Edition). Chapman and Hall, London.Google Scholar
Benjamin, S. (1980). Solvency and profitability in insurance. Transactions of the 21st International Congress of Actuaries, 1, 3346.Google Scholar
Biger, N. & Kahane, Y. (1978). Risk considerations in insurance ratemaking. Journal of Risk and Insurance, 45, 121–32.CrossRefGoogle Scholar
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 631–57.Google Scholar
Brender, A. U. (1988). Solvency testing for life insurers in Canada. Transactions of the 23rd International Congress of Actuaries, 1, 4959.Google Scholar
Brender, A. U. (1988a). ‘Solvency testing for life insurance companies in Canada.’ Paper presented to special meeting on Capital Needs of Insurance Companies, 9 July 1988, Helsinki.Google Scholar
Brown, S. (1851). On the fires in London during the 17 years from 1833 to 1849 inclusive, showing the numbers which occurred in different trades, and the principal causes by which they were occasioned. J.I.A. 1, 3162.Google Scholar
Campbell, R. D. & Clarke, H. E. (1982). Should actuaries be random? J.I.A.S.S. 25, 47112.Google Scholar
Casualty Actuarial Society Committee On Valuation Principles (1988). Statement of valuation principles.Google Scholar
Cooper, R. W. (1974). Investment return and property-liability insurance rate-making. Richard D. Irwin, Homewood, IL.Google Scholar
Coutts, S. M. & Devitt, E. R. F. (1988). Simulation models and the management of a reinsurance company. Transactions of the 23rd International Congress of Actuaries, 1, 109–17.Google Scholar
Cummins, J. D. & Chang, L. (1983). An analysis of the New Jersey formula for including investment income in property liability insurance ratemaking. Journal of Insurance Regulation, 1983, 555-73.Google Scholar
Cummins, J. D. & Harrington, S. E. (1985). Property-liability insurance rate regulation: estimation of underwriting betas using quarterly profit data. Journal of Risk and Insurance, 52, 1643.CrossRefGoogle Scholar
Cummins, J. D. & Harrington, S. E. (1987). Fair rate of return in property-liability insurance. Kluwer Academic Publishers, Norwell, MA.CrossRefGoogle Scholar
Cummins, J. D. (1988). Risk-based premiums for insurance guaranty funds. Journal of Finance, 43, 3.Google Scholar
Cummins, J. D. (1988a). ‘Capital structure and fair profits in property-liability insurance.’ Paper presented to Second International Conference on Insurance Solvency, Brighton U.K., May 1988.Google Scholar
Cummins, J. D. & Derrig, R. A. (1989). Financial models of insurance solvency. Kluwer Academic Publishers, Norwell, MA.CrossRefGoogle Scholar
D’arcy, S. P. (1988). ‘Financial Economics.’ Paper presented to Seminar at the Institute of Actuaries, London, March 1988.Google Scholar
D’arcy, S. P. & Doherty, N. A. (1988). The financial theory of pricing property-liability insurance contracts. Richard D. Irwin. Harewood, IL.Google Scholar
Daykin, C. D., Devitt, E. R. F., Khan, M. R. & McCaughan, J. P. (1984). The solvency of general insurance companies. J.I.A., 111, 279.Google Scholar
Daykin, C. D. & Bernstein, G. D. (1985). ‘A simulation model to examine questions of solvency in the light of asset and run-off risks.’ Paper presented to ASTIN Colloquium in Biarritz, October 1985.Google Scholar
Daykin, C. D.. Bernstein, G. D., Coutts, S. M., Devitt, E. R. F., Hey, G. B., Reynolds, D. I. W. & Smith, P. D. (1987). The solvency of a general insurance company in terms of emerging costs. ASTIN Bulletin, 17, 1, 85132.CrossRefGoogle Scholar
Daykin, C. D., Bernstein, G. D., Coutts, S. M., Devitt, E. R. F., Hey, G. B., Reynolds, D. I. W. & Smith, P. D. (1987a). Assessing the solvency and financial strength of a general insurance company. J.I.A. 114, 227310.Google Scholar
Daykin, C. D. & Hey, G. B. (1988). ‘A management model of a general insurance company using simulation techniques.’ Paper presented to the Second International Conference on Insurance Solvency, Brighton, May 1988 and to the special meeting on Capital Needs of Insurance Companies, 9 July 1988, Helsinki.Google Scholar
Daykin, C. D. & Hey, G. B. (1989). ‘A practical risk theory model for the management of uncertainty in a general insurance company.’ Paper presented to the ASTIN Colloquium in New York in November 1989.Google Scholar
Daykin, C. D. & Hey, G. B. (1989a). ‘Modelling the operations of a general insurance company by simulation.’ Paper presented to the joint IMA/Institute of Actuaries/Faculty of Actuaries Seminar, Staple Inn, July 1989. J.I.A. 116, 639.Google Scholar
Derrig, R. A. (1983). ‘The use of investment income in Massachusetts private passenger automobile and workers' compensation ratemaking.’ Paper presented to the Workers’ Compensation Rating Organizations Meeting on 11 May 1983 (reprinted in Cummins & Harrington, 1987).Google Scholar
Doherty, N. A. & Garven, J. R. (1986). Price regulation in property-liability insurance: a contingent claims approach. Journal of Finance, 41, 5, 1031–50.Google Scholar
Fairley, W. B. (1979). Investment income and profit margins in property-liability insurance: theory and empirical results. Bell Journal of Economics, 10 (Spring), 192-210 (reprinted in Cummins & Harrington, 1987).Google Scholar
Fine, A. E. M., Headdon, C. P., Hewitson, T. W. et al. (1988). Proposals for the statutory basis of valuation of the liabilities of linked long-term insurance business. J.I.A., 115, 556613.Google Scholar
Fisher, L. & Lorie, J. H. (1977). A half century of returns on stocks and bonds; rates of return on investments in common stocks and on U.S. Treasury securities, 1926-1976. University of Chicago School of Business.Google Scholar
Gisg Working Party On Discounting (1987). Paper presented to the General Insurance Study Group Convention, Torquay, October 1987.Google Scholar
Hey, G. B. & Bernstein, G. D. (1988). Cash flow simulation of a general insurance company: Program description. Institute of Actuaries.Google Scholar
Hey, G. B. & Bernstein, G. D. (1988a). Simulating the cash flow of a general insurer. Transactions of the 23rd International Congress of Actuaries, 1, 243–58.Google Scholar
Hill, R. D. (1979). Profit regulation in property-liability insurance. Bell Journal of Economics, 10, (Spring), 172–91.Google Scholar
Hill, R. D. & Modigliani, F. (1981). ‘The Massachusetts model of profit regulation in non life insurance: an appraisal and extensions.’ Paper prepared for the 1982 Massachusetts automobile rate hearings (reprinted in Cummins & Harrington, 1987).Google Scholar
Kahane, Y. (1979). Solidity, leverage and the regulation of insurance companies. The Geneva Papers on Risk and Insurance, 4, December 1979, 319.Google Scholar
Kitts, A. (1988). Applications of stochastic financial models: a review. University of Southampton.Google Scholar
Kits, A. (1990). Comments on a model or retail price inflation. J.I.A. 117, 407.Google Scholar
Kraus, A. & Ross, S. A. (1982). The determination of fair profits for the property-liability insurance firm. Journal of Finance, 37, 4, 1015–28 (reprinted in Cummins & Harrington, 1987).Google Scholar
Lance, W. (1852). Paper upon marine assurance. Presented to the Institute of Actuaries in May 1852. J.I.A. 2, 362–76.Google Scholar
Larner, K., Akhurst, R., Bennett, M. et al. (1989). ‘Actuarial Reporting in General Insurance.’ Paper presented to the General Insurance Study Group Convention, Brighton, October 1989.Google Scholar
Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47 (February), 1337.Google Scholar
Lintner, J. (1965a) Security prices, risk and maximal gains from diversification. Journal of Finance, 20, 587615.Google Scholar
Lee, R. E. (1985). A prophet of profits. J.I.A.S.S. 28, 142.Google Scholar
Markowitz, H. (1959). Portfolio selection. Cowles Monograph No. 16. John Wiley, New York.Google Scholar
Moorhead, E. J. (1989). Our yesterdays: The history of the actuarial profession in North America, 1809-1979. Society of Actuaries.Google Scholar
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34, 768–83.CrossRefGoogle Scholar
Myers, S. C. (1972). The application of finance theory in public utility cases. Bell Journal of Economics, 3 (Spring) 5897.Google Scholar
Myers, S. C. (1972a). On the use of beta in regulatory proceedings. A comment. Bell Journal of Economics, 3 (Autumn), 622–7.Google Scholar
Myers, S. C. & Cohn, R. A. (1981). ‘Insurance rate of return regulation and the capital asset pricing model.’ Paper prepared for the 1982 Massachusetts automobile rate hearings (reprinted as ‘A discounted cash flow approach to property-liability insurance rate regulation’ in Cummins & Harrington, 1987).Google Scholar
Paulson, A. S. & Deekshit, R. V. (1986). ‘Flow models for premium and surplus analysis.’ Paper presented to the First International Conference on Insurance Solvency, Philadelphia U.S.A., June 1986 (published in Cummins & Derrig, 1989).Google Scholar
Paulson, A. S. (1988). ‘Assessment via simulation of certain financial rate of return models, CAPM and duration matching.’ Paper presented to the Second International Conference on Insurance Solvency, Brighton U.K., May 1988.Google Scholar
Pentikäinen, T. & Rantala, J. (1982). Solvency of insurers and equalization reserves. Helsinki.Google Scholar
Pentikäinen, T. & Rantala, J. (1986). Run-off risk as part of claims fluctuation. ASTIN Bulletin 16, 2, 113–47.Google Scholar
Pentikäinen, T., Bonsdorff, H., Pesonen, M., Rantala, J. & Ruohonen, M. (1989). Insurance solvency and financial strength. Helsinki.Google Scholar
Pettway, R. H. (1978). On the use of beta in regulatory proceedings. An empirical examination. Bell Journal of Economics, 9 (Spring), 239–48.Google Scholar
Purchase, D. E., Fine, A. E. M., Headdon, C. P. et al. (1989). Reflections on resilience—some considerations of mismatching tests, with particular reference to non-linked long-term insurance business. J.I.A. 116, 347.Google Scholar
Quirin, G. D. & Waters, W. R. (1975). Market efficiency and the cost of capital: the strange case of fire and casualty insurance companies. Journal of Finance 30 (May), 427–50.CrossRefGoogle Scholar
Rantala, J. (1984). An application of stochastic control theory to insurance business. Acta Universitatis Tamperensis Series A, 164.Google Scholar
Rantala, J. (1986). ‘Methods for analysing the effects of the underwriting risk on the insurer's long-term solvency.’ Paper presented to the First International Conference on Insurance Solvency, Philadelphia U.S.A. (published in Cummins & Derrig, 1989).Google Scholar
Rantala, J. (1988). Frequency response functions—a technique to evaluate the variation range in certain insurance indicators. Transactions of the 23rd International Congress of Actuaries, 1, 453–68.Google Scholar
Rantala, J. (1988a). ‘Fluctuations in insurance business results.’ Lecture of introduction to Session 1 of the 23rd International Congress of Actuaries, Helsinki.Google Scholar
Redington, F. M. (1952). Review of the principles of life office valuations. J.I.A. 78, 286315.Google Scholar
Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13, 341–60.CrossRefGoogle Scholar
Rubinstein, M. (1976). The valuation of uncertain income streams and the pricing of options. Bell Journal of Economics, 7 (Autumn), 407–25.CrossRefGoogle Scholar
Smart, I. C. (1977). Pricing and profitability in a life office. J.I.A. 104, 125–58.Google Scholar
Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance, 19 (September), 425–42.Google Scholar
Taylor, G. C. (1988). ‘An analysis of underwriting cycles in relation to insurance pricing and solvency.’ Paper presented to the Second International Conference on Insurance Solvency, Brighton U.K., May 1988.Google Scholar
Tilley, J. A. (1988). ‘The application of modern techniques to the investment of insurance and pension funds.’ Lecture of introduction to Session 5 of the 23rd International Congress of Actuaries, Helsinki.Google Scholar
Wilkie, A. D. (1984). Steps towards a comprehensive stochastic investment model. Occasional Actuarial Research Discussion Paper No. 36, Institute of Actuaries.Google Scholar
Wilkie, A. D. (1986). A stochastic investment model for actuarial use. T.F.A., 39, 341–73.Google Scholar
Wilkie, A. D. (1988). A stochastic model for property investment (personal communication).Google Scholar
Wise, A. J. (1984). The matching of assets to liabilities. J.I.A. 111, 445–86.Google Scholar
Wise, A. J. (1987). Matching and portfolio selection: Part 1. J.I.A. 114, 113–34.Google Scholar
Wise, A. J. (1987a). Matching and portfolio selection: Part 2. J.I.A. 114, 551–68.Google Scholar