Equity-Indexed life insurance: Pricing and reserving using the principle of equivalent utility

North American Actuarial Journal

Volumn 7, Issue 1, 2003, Pages 68-86

  Young, Virginia R ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85011227165     PISSN: 10920277     EISSN: None     Source Type: Journal    
DOI: 10.1080/10920277.2003.10596078     Document Type: Article

References (45)

1. AASE, K. K., AND S.-A. PERSSON. 1994. “Pricing of Unit-Linked Life Insurance Policies,” Scandinavian Actuarial Journal (1): 26–52.
2. AMERICAN ACADEMY OF ACTUARIES (AAA). 1998. “Response of the American Academy of Actuaries to the Securities and Exchange Commission,” Concept Release No. 33–7438, File number S7–22–97. Washington, DC: American Academy of Actuaries.
3. AMERICAN ACADEMY OF ACTUARIES (AAA) 1999a. “Special Issues for Equity Indexed Products,” Life Practice Note, July. Washington, DC: American Academy of Actuaries.
4. AMERICAN ACADEMY OF ACTUARIES (AAA) 1999b. “Report of the American Academy of Actuaries’ Equity Indexed Universal Life Work Group to the Life and Health Actuarial Task Force of the NAIC,” October. Washington, DC: American Academy of Actuaries
5. Bacinello, A. R., and F. Ortu. 1993. “Pricing Equity-Linked Life Insurance with Endogenous Minimum Guarantees,” Insurance: Mathematics and Economics 12(3): 245-57.
6. Bacinello, A. R., and F. Ortu. 1994. “Single and Periodic Premiums for Guaranteed Equity-Linked Life Insurance under Interest-Rate Risk: The ”Lognormal + Vasicek“ Case,” in Financial Modeling, pp. 1-25, edited by L. Peccati and M. Viren. Heidelberg, Germany: Physica-Verlag.
7. Barles, G., and H. M. Soner. 1998. “Option Pricing with Transaction Costs and a Nonlinear Black-Scholes Equation,” Finance and Stochastics 2(4): 369-97.
8. BjOrk, T. 1998. Arbitrage Theory in Continuous Time. New York: Oxford University Press.
9. Black, F., and M. Sgholes. 1973. “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81(3): 637-54.
10. Borcii, K. 1963. “Recent Developments in Economic Theory and their Application to Insurance,” ASTIN Bulletin 2(3): 322-341.
11. Bowers, N. L., II. U. Gerber, J. C. Hickman, D. A. Jones, and C. J. Nesbitt. 1997. Actuarial Mathematics. 2nd ed. Schaumburg, IL: Society of Actuaries.
12. Boyle, P. P., and E. S. Schwartz. 1977. “Equilibrium Prices of Guarantees under Equity-Linked Contracts,” Journal of Risk and Insurance 44(4): 639-660.
13. Brennan, M. J., and E. S. Schwartz. 1976. “The Pricing of Equity- Linked Life Insurance Policies with an Asset Value Guarantee,” Jourtud of Financial Economics, 3(3): 195-213.
14. Brennan, M. J., and E. S. Schwartz. 1979. “Alternative Investment Strategies for the Issuers Of Equity Linked Life Insurance Policies with an Asset Value Guarantee,” Journal of Busitiess 52(1): 63-93.
15. Chan, F. Y., and E. W. Shiu. 1982. “Underwriting Gain as a Random Variable,” Actuarial Research Clearing House (2): 5-9.
16. Davis, M. H. A., V. G. Panas, and T. Zaripiiopoulou. 1993. “European Option Pricing with Transaction Costs,” SIAM Journal on Control and Optimization 31(2): 470-93.
17. Davis, M. II. A., and T. Zaripiiopoulou. 1995. “American Options and Transaction Fees,” in Mathematical Finance, IMA Vol. 65, pp. 47-62, edited by M. Davis, D. Duffie, W. Fleming and S. Shreve. New York: Springer-Verlag
18. DuChateau, P., and D. W. Zacilmann. 1986. Partial Differential Equations in Schaum 's Outline Series. New York: McGraw-Hill.
19. Ekern, S., and S.-A. Persson. 1996. “Exotic Unit-Linked Life Insurance Contracts,” Geneva Papers on Risk and Insurance Theory 21(1): 35-63.
20. Fitzpatrick, B., and W. H. Fleming. 1991. “Numerical Methods for an Optimal Investment-Consumption Model,” Mathematics of Operations Research 16(4): 832-41.
21. Fleming, W. H., and H. M. Soner. 1993. Controlled Markov Processes and Viscosity Solutions, Applications of Mathematics, 25. New York: Springer-Verlag.
22. Föllmer, H., and M. Schweizer. 1988. “Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading, ASTIN Bulletin 18(2): 147-60.
23. Fraser, J. C., W. N. Miller, and C. M. Sternhell. 1969. “Analysis of Basic Actuarial Theory for Fixed Premium Variable Benefit Life Insurance, with Discussion,” Transactions of the Society of Actuaries 21(1): 343-457.
24. Gerber, H. U. 1974. “On Additive Premium Calculation Principles,” ASTIN Bulletin 7(3): 215-22.
25. Gerber, H. U. 1976. “A Probabilistic Model for (Life) Contingencies and a Delta-Free Approach to Contingency Reserves,” with discussion, Transactions of the Society of Actuaries 28: 127-48.
26. Gerber, H. U., and G. Pafumi. 1998. “Utility Functions: From Risk Theory to Finance,” with discussion, North American Actuarial Journal 2(3): 74-100.
27. Hodges, S. D., and A. Neuberger. 1989. “Optimal Replication of Contingent Claims under Transaction Costs,” Review of Futures Markets 8(2): 222-39.
28. st International Congress of Actuaries, Vol. 8: 87-141.
29. Mazaiieri, M. 2001. “Reservation Prices with Stochastic Volatility.” Ph.D. Dissertation, School of Business, University of Wisconsin-Madison.
30. Merton, R. C. 1971. “Optimum Consumption and Portfolio Rules in a Continuous-Time Model,” Journal of Economic Theory 3(4): 373-413.
31. Merton, R. C. 1992. Coïitinuous-Time Finance. Revised ed. Cambridge, MA: Blackwell.
32. Möller, T. 1998. “Risk-Minimizing Hedging Strategies for Unit- Linked Life Insurance Contracts,” ASTIN Bulletin 28(1): 17-47.
33. Möller, T. 2001. “Hedging of Equity-Linked Life Insurance Contracts,” North American Actuarial Journal 5(2): 79-95.
34. Moore, K. S., and V. R. Young. 2002. “Pricing Equity-Linked Pure Endowments via the Principle of Equivalent Utility.” Working paper, Department of Mathematics, University of Michigan, Ann Arbor, Michigan.
35. Musiela, M., and T. Zaripiiopoulou. 2002. “Indifference Prices and Related Measures.” Working paper, Department of Mathematics, University of Texas at Austin.
36. Nielsen, J. A., and K. Sandmann. 1995. “Equity-Linked Life Insurance: A Model With Stochastic Interest Rates,” Iîisurance: Mathematics and Economics 16(3): 225-53.
37. Persson, S.-A. 1993. “Valuation of a Multistate Life Insurance Contract with Random Benefits,” Scandinavian Journal of Management, 9(Supplement): S73-S86.
38. Pratt, J. W. 1964. “Risk Aversion in the Small and in the Large, Econometrica 32: 122-36.
39. Tiong, S. 2000. “Valuing Equity-Indexed Annuities,” with discussion, North American Actuarial Journal 4(4): 149-70.
40. Tourin, A., and T. Zaripiiopoulou. 1994. “Numerical Schemes for Investment Models with Singular Transactions,” Computational Economics 7(4): 287-307.
41. Wang, S. 1995. “Insurance Pricing and Increased Limits Rate- making by Proportional Hazards Transforms,” Insurance: Mathematics and Economics 17(1): 43-54.
42. Young, V. R., and K. S. Moore. 2002. “Optimal Insurance in a Continuous-Time Model.” Working paper, School of Business, University of Wisconsin-Madison.
43. Young, V. R., and T. Zariphopoulou. 2000. “Computation of Distorted Probabilities for Diffusion Processes via Stochastic Control Methods,” Insurance: Mathematics and Economics 27(1): 1-18.
44. Young, V. R., and T. Zariphopoulou. 2002a. “Pricing Dynamic Insurance Risks Using the Principie Of Equivalent Utility,” Scandinavian Actuarial Journal. Forthcoming.
45. Young, V. R., and T. Zariphopoulou. 2002b. “Pricing Insurance via Stochastic Control: Optimal Consumption And Terminal Wealth. Working paper, School of Business, University of Wisconsin-Madison.