## Regression modeling for the valuation of large variable annuity portfolios.(English)Zbl 1393.91099

Summary: Variable annuities are insurance products that contain complex guarantees. To manage the financial risks associated with these guarantees, insurance companies rely heavily on Monte Carlo simulation. However, using Monte Carlo simulation to calculate the fair market values of these guarantees for a large portfolio of variable annuities is extremely time consuming. In this article, we propose the class of GB2 distributions to model the fair market values of guarantees to capture the positive skewness typically observed empirically. Numerical results are used to demonstrate and evaluate the performance of the proposed model in terms of accuracy and speed.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics 91G20 Derivative securities (option pricing, hedging, etc.)

### Keywords:

regression modeling; large variable annuity portfolios

### Software:

Latin Hypercube Sampling; clhs
Full Text:

### References:

 [1] Barton, R. R., Proceedings of the 2015 Winter Simulation Conference, Tutorial: simulation metamodeling, 1765-1779, (2015), IEEE Press, Piscataway, NJ [2] Bauer, D.; Kling, A.; Russ, J., A universal pricing framework for guaranteed minimum benefits in variable annuities, ASTIN Bulletin, 38, 2, 621-651, (2008) · Zbl 1274.91399 [3] Beirlant, J.; Goegebeur, Y.; Segers, J.; Teugels, J., Statistics of Extremes: Theory and Applications, (2004), Wiley, West Sussex, UK [4] Bélanger, A.; Forsyth, P.; Labahn, G., Valuing the guaranteed minimum death benefit clause with partial withdrawals, Applied Matehmatical Finance, 16, 6, 451-496, (2009) · Zbl 1189.91066 [5] Boyle, P.; Hardy, M., Reserving for maturity guarantees: two approaches, Insurance: Mathematics and Economics, 21, 2, 113-127, (1997) · Zbl 0894.90044 [6] Cummins, J.; Dionne, G.; McDonald, J. B.; Pritchett, B., Applications of the GB2 family of distributions in modeling insurance loss processes, Insurance: Mathematics and Economics, 9, 4, 257-272, (1990) [7] Dai, M.; Kwok, Y.; Zong, J., Guaranteed minimum withdrawal benefit in variable annuities, Mathematical Finance, 18, 4, 595-611, (2008) · Zbl 1214.91052 [8] Frees, E. W., Regression Modeling with Actuarial and Financial Applications, (2009), Cambridge University Press, Cambridge · Zbl 1284.62010 [9] Frees, E. W.; Valdez, E. A., Hierarchical insurance claims modeling, Journal of the American Statistical Association, 103, 484, 1457-1469, (2008) · Zbl 1286.62087 [10] Friedman, L. W.; Gass, S.; Fu, M., Encyclopedia of Operations Research and Management Science, Simulation metamodeling, 1404-1410, (2013), Springer, New York [11] Gan, G., Application of data clustering and machine learning in variable annuity valuation, Insurance: Mathematics and Economics, 53, 3, 795-801, (2013) · Zbl 1290.91086 [12] Gan, G., Application of metamodeling to the valuation of large variable annuity portfolios, Proceedings of the Winter Simulation Conference, 1103-1114, (2015), IEEE Press, Piscataway, NJ [13] Gan, G., A multi-asset Monte Carlo simulation model for the valuation of variable annuities, Proceedings of the Winter Simulation Conference, 3162-3163, (2015), IEEE Press, Piscataway, NJ [14] Gan, G.; Lin, X. S., Valuation of large variable annuity portfolios under nested simulation: A functional data approach, Insurance: Mathematics and Economics, 62, 138-150, (2015) · Zbl 1318.91112 [15] Gan, G.; Lin, X. S., Efficient Greek calculation of variable annuity portfolios for dynamic hedging: A two-level metamodeling approach, North American Actuarial Journal, 21, 2, 161-177, (2017) [16] Variable annuities—an analysis of financial stability, (2013) [17] Isaaks, E.; Srivastava, R., An Introduction to Applied Geostatistics, (1990), Oxford University Press, Oxford [18] Kleiber, C.; Kotz, S., Statistical Size Distributions in Economics and Actuarial Sciences, (2003), Wiley, Hoboken, NJ · Zbl 1044.62014 [19] Liang, Z.; Sheng, W., Valuing inflation-linked death benefits under a stochastic volatility framework, Insurance: Mathematics and Economics, 69, 45-58, (2016) · Zbl 1369.91184 [20] Loeppky, J. L.; Sacks, J.; Welch, W. J., Choosing the sample size of a computer experiment: A practical guide, Technometrics, 51, 4, 366-376, (2009) [21] Luo, X.; Shevchenko, P. V., Valuation of variable annuities with guaranteed minimum withdrawal and death benefits via stochastic control optimization, Insurance: Mathematics and Economics, 62, 5-15, (2015) · Zbl 1318.91117 [22] Marshall, C.; Hardy, M.; Saunders, D., Valuation of a guaranteed minimum income benefit, North American Actuarial Journal, 14, 1, 38-59, (2010) [23] Milevsky, M.; Posner, S., The titanic option: valuation of the guaranteed minimum death benefit in variable annuities and mutual funds, Journal of Risk and Insurance, 68, 1, 93-128, (2001) [24] Millar, R. B., Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB, (2011), Wiley, West Sussex, UK · Zbl 1273.62012 [25] Minasny, B.; McBratney, A. B., A conditioned Latin hypercube method for sampling in the presence of ancillary information, Computers & Geosciences, 32, 9, 1378-1388, (2006) [26] Myung, I. J., Tutorial on maximum likelihood estimation, Journal of Mathematical Psychology, 47, 1, 90-100, (2003) · Zbl 1023.62112 [27] Peng, J.; Leung, K. S.; Kwok, Y. K., Pricing guaranteed minimum withdrawal benefits under stochastic interest rates, Quantitative Finance, 12, 6, 933-941, (2012) · Zbl 1279.91165 [28] Rasmussen, C.; Williams, C., Gaussian Processes for Machine Learning, (2005), MIT Press, Cambridge, MA [29] Roudier, P., clhs: A R Package for Conditioned Latin Hypercube Sampling, (2011) [30] Sun, J.; Frees, E. W.; Rosenberg, M. A., Heavy-tailed longitudinal data modeling using copulas, Insurance: Mathematics and Economics, 42, 2, 817-830, (2008) · Zbl 1152.91605
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.