1,745
Views
5
CrossRef citations to date
0
Altmetric
Research Article

Time-consistent and market-consistent actuarial valuation of the participating pension contract

ORCID Icon & ORCID Icon
Pages 266-294 | Received 15 Jul 2020, Accepted 01 Oct 2020, Published online: 26 Oct 2020

References

  • Acciaio, B. & Penner, I. (2011). Dynamic convex risk measures. In Di Nunno G., & Øksendal B., editors, Advanced Mathematical Methods for Finance. Berlin: Springer.
  • Angelis, P. D., Martire, A. L. & Russo, E. (2014). A bivariate model for evaluating equity-linked policies with surrender option. Scandinavian Actuarial Journal 2016(3), 246–261.
  • Artzner, P., Delbaen, F., Eber, J., Heath, D. & Ku, H. (2007). Coherent multiperiod risk adjusted values and Bellman's principle. Annals of Operations Research 152(1), 5–22.
  • Bacinello, A. R. (2003). Pricing guaranteed life insurance participating policies with annual premiums and surrender option. North American Actuarial Journal 7, 1–17.
  • Bacinello, A. R., Biffis, E. & Millossovich, P. (2010). Regression-based algorithms for life insurance contracts with surrender guarantees. Quantitative Finance 10, 1077–1090.
  • Bacinello, A. R., Millossovich, P., Olivieri, A. & Pitacco, E. (2011). Variable annuities: a unifying valuation approach. Insurance: Mathematics and Economics 49, 285–297.
  • Barigou, K. & Dhaene, J. (2019). Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting. Scandinavian Actuarial Journal 2019(2), 163–187.
  • Barigou, K., Chen, Z. & Dhaene, J. (2019). Fair dynamic valuation of insurance liabilities: merging actuarial judgement with market- and time-consistency. Insurance: Mathematics and Economics 88, 19–29.
  • Bernard, C., Courtois, O. L. & Quittard-Pinon, F. (2005). Market value of life insurance contracts under stochastic interest rates and default risk. Insurance: Mathematics and Economics 36, 499–516.
  • Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659.
  • Cairns, A., Blake, D. & Dowd, K. (2006). Pricing death: frameworks for the valuation and securitization of mortality risk. Astin Bulletin 36(1), 79–120.
  • Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A. & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal 13(1), 1–35.
  • Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D. & Khalaf-Allah, M. (2011). Mortality density forecasts: an analysis of six stochastic mortality models. Insurance: Mathematics and Economics 48, 355–367.
  • Carriere, J. (1996). Valuation of the early-exercise price for options using simulations and nonparametric regression. Insurance: Mathematics and Economics 19(1), 19–30.
  • Chen, Z., Chen, B. & Dhaene, J. (2020). Fair dynamic valuation of insurance liabilities: a loss averse convex hedging approach. Scandinavian Actuarial Journal 1–27.
  • Cheridito, P. & Kupper, M. (2011). Composition of time-consistent dynamic monetary risk measures in discrete time. International Journal of Theoretical and Applied Finance 14.
  • Cheridito, P. & Stadje, M. (2009). Time-inconsistency of var and time-consistent alternatives. Finance Research Letters 6(1), 40–46.
  • Cheridito, P., Delbaen, F. & Kupper, M. (2006). Dynamic monetary risk measures for bounded discrete-time processes. Electronic Journal of Probability 11(3), 57–106.
  • Deelstra, G., Devolder, P., Gnameho, K. & Hieber, P. (2019). Valuation of hybrid financial and actuarial products in life insurance: a universal 3-step method. Available at SSRN: https://ssrn.com/abstract=3307061.
  • Delong, L., Dhaene, J. & Barigou, K. (2019a). Fair valuation of insurance liability cash-flow streams in continuous time: applications. ASTIN Bulletin 49(2), 299–333.
  • Delong, L., Dhaene, J. & Barigou, K. (2019b). Fair valuation of insurance liability cash-flow streams in continuous time: theory. Insurance: Mathematics and Economics 88, 196–208.
  • Dhaene, J., Stassen, B., Barigou, K., Linders, D. & Chen, Z. (2017). Fair valuation of insurance liabilities: merging actuarial judgement and market-consistency. Insurance: Mathematics and Economics 76, 14–27.
  • Follmer, H. & Penner, I. (2006). Convex risk measures and the dynamics of their penalty functions. Statistics & Decisions 24(1), 61–96.
  • Glasserman, P. (2004). Monte Carlo methods in financial engineering. New York: Springer-Verlag.
  • Glasserman, P. & Yu, B. (2004a). Number of paths versus number of basis functions in American option pricing. The Annals of Applied Probability 14(4), 2090–2119.
  • Glasserman, P. & Yu, B. (2004b). Pricing american options by simulation: regression now or regression later? In Niederreiter, H., editor, Monte Carlo and Quasi-Monte Carlo methods in scientific computing. Berlin: Springer Verlag. P. 213–226.
  • Grosen, A. & Jorgensen, P. L. (2000). Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics 26, 37–57.
  • Hull, J. & White, A. (1996). Using hull-white interest rate trees. The Journal of Derivatives 3(3), 26–36.
  • Jobert, A. & Rogers, L. (2008). Valuations and dynamic convex risk measures. Mathematical Finance 18(1), 1–22.
  • Kleinow, T. (2009). Valuation and hedging of participating life-insurance policies under management discretion. Insurance: Mathematics and Economics 44, 78–87.
  • Kupper, M., Cheridito, P. & Filipovic, D. (2008). Dynamic risk measures, valuations and optimal dividends for insurance. In Mini-workshop: mathematics of solvency. Mathematisches Forschungsinstitut Oberwolfach.
  • Lee, R. D. & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87(419), 659–671.
  • Létourneau, P. & Stentoft, L. (2014). Refining the least squares Monte Carlo method by imposing structure. Quantitative Finance 14, 495–507.
  • Li, J. & Szimayer, A. (2014). The effect of policyholders? Rationality on unit-linked life insurance contracts with surrender guarantees. Quantitative Finance 14, 327–342.
  • Longstaff, F. A. & Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-squares approach. Review of Financial Studies 14(1), 113–147.
  • Madan, D. & Milne, F. (1994). Contingent claims valued and hedged by pricing and investing in a basis. Mathematical Finance 4(3), 223–245.
  • Malamud, S., Trubowitz, E. & Wüthrich, M. (2008). Market consistent pricing of insurance products. ASTIN Bulletin 38(2), 483–526.
  • Møller, T. (2002). On valuation and risk management at the interface of insurance and finance. British Actuarial Journal 8(4), 787–827.
  • Musiela, M. & Zariphopoulou, T. (2004). A valuation algorithm for indifference prices in incomplete markets. Finance and Stochastics 8(3), 399–414.
  • Pelsser, A. (2000). Efficient methods for valuing interest rate derivatives. London: Springer Verlag.
  • Pelsser, A. & Stadje, M. (2014). Time-consistent and market-consistent evaluations. Mathematical Finance 24(1), 25–65.
  • Penner, I. (2007). Dynamic convex risk measures: time consistency, prudence, and sustainability. PhD thesis, Humboldt-Universität zu Berlin.
  • Renshaw, A. E. & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics 38, 556–570.
  • Roorda, B., Schumacher, J. & Engwerda, J. (2005). Coherent acceptability measures in multiperiod models. Mathematical Finance 15(4), 589–612.
  • Rosazza Gianin, E. (2006). Risk measures via g-expectations. Insurance: Mathematics and Economics 39(1), 19–34.
  • Salahnejhad, A. & Pelsser, A. (2016). Time-consistent actuarial valuation. Insurance: Mathematics and Economics 66, 97–112.
  • Salahnejhad, A. & Pelsser, A. (2020). Market-consistent actuarial valuations with applications to EIOPA risk-margin and time-consistent pricing. Under Review, Graduate School of Business and Economics, Maastricht University.
  • Shreve, S. E. (2010). Stochastic calculus for finance II, continuous-time models. New York: Springer Finance.
  • Stadje, M. (2010). Extending dynamic convex risk measures from discrete time to continuous time: a convergence approach. Insurance: Mathematics and Economics 47(3), 391–404.
  • Stentoft, L. (2004). Convergence of the least squares Monte Carlo approach to American option valuation. Management Science 50, 1193–1203.
  • Tanskanen, A. J. & Lukkarinen, J. (2003). Fair valuation of path-dependent participating life insurance contracts. Insurance: Mathematics and Economics 33, 595–609.
  • Zaglauer, K. & Bauer, D. (2008). Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment. Insurance: Mathematics and Economics 43, 29–40.