Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates

Insurance: Mathematics and Economics

Volumn 42, Issue 1, 2008, Pages 14-30

  Ludkovski, Michael ^a   Young, Virginia R ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Exponential utility; Indifference pricing; Mortality contingent claims; Nonlinear expectations; Stochastic mortality

Indexed keywords

EID: 38649085646     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2006.11.009     Document Type: Article

References (39)

1. Becherer D. Rational hedging and valuation of integrated risks under constant absolute risk aversion. Insurance: Mathematics and Economics 33 1 (2003) 1-28
2. Bielecki, T., Jeanblanc, M., 2004. Indifference pricing of defaultable claims. Technical Report. Illinois Institute of Technology
3. Biffis E. Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics 37 3 (2005) 443-468
4. Björk T. Arbitrage Theory in Continuous Time (1998), Oxford University Press, Oxford
5. Blanchet-Scalliet C., El Karoui N., and Martellini L. Dynamic asset pricing theory with uncertain time-horizon. Journal of Economic Dynamics and Control 29 (2005) 1737-1764
6. Bouchard B., and Touzi N. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stochastic Processes and Applications 111 2 (2004) 175-206
7. Cairns, A.J.G., Blake, D., Dowd, K., 2004. Pricing framework for securitization of mortality risk. Working paper, Heriot-Watt University
8. Carmona, R., Ludkovski, M., 2005. Optimal switching with applications to energy tolling agreements. Technical report, Princeton University
9. Carrière J.F. Valuation of the early-exercise price for options using simulations and nonparametric regression. Insurance: Mathematics and Economics 19 1 (1996) 19-30
10. Dahl M. Stochastic mortality in life insurance: Market reserves and mortality-linked insurance contracts. Insurance: Mathematics and Economics 35 1 (2004) 113-136
11. Dahl M., and Møller T. Valuation and hedging of life insurance liabilities with systematic mortality risk. Insurance: Mathematics and Economics 39 2 (2006) 193-217
12. Davis M.H.A., Panas V.G., and Zarphipoulou T. European option pricing with transaction costs. SIAM Journal on Control and Optimization 31 (1993) 470-493
13. DiLorenzo, E., Sibillo, M., 2003. Longevity risk: Measurement and application perspectives. Working paper, Università degli Studi di Napoli
14. Gobet E., Lemor J., and Warin X. Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations. Bernoulli 12 5 (2006) 889-916
15. Henderson V. Valuation of claims on nontraded assets using utility maximization. Mathematical Finance 12 4 (2002) 351-373
16. Henderson, V., 2005. Valuing the option to invest in an incomplete market. Working paper, Princeton University
17. Henderson, V., Hobson, D., 2005. Utility indifference pricing - an overview. In: Carmona, R. (Ed.), Volume on Indifference Pricing. Princeton University Press (in press)
18. Hodges S.D., and Neuberger A. Optimal replication of contingent claims under transaction costs. Review of Futures Markets 8 (1989) 222-239
19. Ilhan, A., Jonsson, M., Sircar, R., 2004. Portfolio optimization with derivatives and indifference pricing. In: Carmona, R. (Ed.), Volume on Indifference Pricing. Princeton University Press (in press)
20. Karatzas I., and Shreve S.E. Brownian Motion and Stochastic Calculus. second edn (1991), Springer-Verlag, New York
21. Kushner H.J., and Dupuis P. Numerical Methods for Stochastic Control Problems in Continuous Time. second edn (2001), Springer-Verlag, New York
22. Lamberton D., and Lapeyre B. Introduction to Stochastic Calculus Applied to Finance (1996), Chapman & Hall/CRC, Boca Raton, Florida
23. Lee R.D., and Carter L.R. Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87 419 (1992) 659-671
24. Leland H.E. Option pricing and replication with transactions costs. Journal of Finance 40 5 (1985) 1283-1301
25. Longstaff F., and Schwartz E.S. Valuing American options by simulations: A simple least squares approach. The Review of Financial Studies 14 (2001) 113-148
26. Ludkovski, M., 2006. Financial hedging of operational flexibility. Working Paper, University of Michigan
27. Milevsky M.A., and Promislow S.D. Mortality derivatives and the option to annuitize. Insurance: Mathematics and Economics 29 3 (2001) 299-318
28. Milevsky, M.A., Promislow, S.D., Young, V.R., 2005. Financial valuation of mortality risk via the instantaneous sharpe ratio. Working paper, University of Michigan
29. Musiela M., and Zariphopoulou T. A valuation algorithm for indifference prices in incomplete markets. Finance and Stochastics 8 3 (2004) 399-414
30. Olivieri A. Uncertainty in mortality projections: An actuarial perspective. Insurance: Mathematics and Economics 29 2 (2001) 231-245
31. Pagès G., Pham H., and Printems J. Optimal quantization methods and applications to numerical problems in finance. Handbook of Computational and Numerical Methods in Finance (2004), Birkhäuser, Boston 253-297
32. Pratt J.W. Risk aversion in the small and in the large. Econometrica 32 (1964) 122-136
33. Schrager D.F. Affine stochastic mortality. Insurance: Mathematics and Economics 38 1 (2006) 81-97
34. Schweizer M. A guided tour through quadratic hedging approaches. In: Jouini E., Cvitanic J., and Musiela M. (Eds). Option Pricing, Interest Rates and Risk Management (2001), Cambridge University Press 538-574
35. Soininen, P., 1995. Stochastic variation of interest and mortality. In: Proceedings of the 5th AFIR International Colloquium, pp. 871-904
36. Walter W. Differential and Integral Inequalities (1970), Springer-Verlag, New York
37. Young V.R., and Zariphopoulou T. Pricing dynamic insurance risks using the principle of equivalent utility. Scandinavian Actuarial Journal 4 (2002) 246-279
38. Young V.R. Equity-indexed life insurance: Pricing and reserving using the principle of equivalent utility. North American Actuarial Journal 7 1 (2003) 68-86
39. Young V.R. Pricing in an incomplete market with an affine term structure. Mathematical Finance 14 3 (2004) 359-381