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Xu, Lin; Shen, Guangjun; Yao, Dingjun

Pricing of equity indexed annuity under fractional Brownian motion model. (English) Zbl 1471.91489

Abstr. Appl. Anal. 2014, Article ID 380718, 9 p. (2014).
Summary: Fractional Brownian motion with Hurst exponent \(H \in(1 / 2, 1)\) is a good candidate for modeling financial time series with long-range dependence and self-similarity. The main purpose of this paper is to address the valuation of equity indexed annuity (EIA) designs under the market driven by fractional Brownian motion. As a result, this paper presents an explicit pricing expression for point-to-point EIA design and bounds for the pricing of high-water-marked EIA design. Some numerical examples are given to illustrate the impact of the parameters involved in the pricing problems.

MSC:

91G05 Actuarial mathematics
60G22 Fractional processes, including fractional Brownian motion
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\textit{L. Xu} et al., Abstr. Appl. Anal. 2014, Article ID 380718, 9 p. (2014; Zbl 1471.91489)
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References:

[1] Marrion, J., 4th quarter index annuity sales
[2] Tiong, S., Valuing equity-indexed annuities, North American Actuarial Journal, 4, 4, 149-163, (2000) · Zbl 1083.62545
[3] Boyle, P.; Tian, W., The design of equity-indexed annuities, Insurance: Mathematics & Economics, 43, 3, 303-315, (2008) · Zbl 1152.91484
[4] Gerber, H. U.; Shiu, E. S. W., Pricing lookback options and dynamic guarantees, North American Actuarial Journal, 7, 1, 48-67, (2003) · Zbl 1084.91507
[5] Hardy, M., Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, (2003), Ontario, Canada: John Wiley & Sons, Ontario, Canada · Zbl 1092.91042
[6] Jaimungal, S., Pricing and hedging equity indexed annuities with variance gamma deviates
[7] Kijima, M.; Wong, T., Pricing of ratchet equity-indexed annuities under stochastic interest rates, Insurance: Mathematics & Economics, 41, 3, 317-338, (2007) · Zbl 1141.91457
[8] Lee, H., Pricing equity-indexed annuities with path-dependent options, Insurance: Mathematics & Economics, 33, 3, 677-690, (2003) · Zbl 1103.91368
[9] Lin, X. S.; Tan, K. S., Valuation of equity-indexed annuities under stochastic interest rates, North American Actuarial Journal, 7, 4, 72-91, (2003) · Zbl 1084.60530
[10] Moore, K. S., Optimal surrender strategies for equity-indexed annuity investors, Insurance: Mathematics & Economics, 44, 1, 1-18, (2009) · Zbl 1156.91379
[11] Biffis, E., Affine processes for dynamic mortality and actuarial valuations, Insurance: Mathematics & Economics, 37, 3, 443-468, (2005) · Zbl 1129.91024
[12] Biffis, E.; Denuit, M.; Devolder, P., Stochastic mortality under measure changes · Zbl 1226.91022
[13] Hainaut, D.; Devolder, P., Mortality modelling with Lévy processes, Insurance: Mathematics & Economics, 42, 1, 409-418, (2008) · Zbl 1141.91516
[14] Jalen, L.; Mamon, R., Valuation of contingent claims with mortality and interest rate risks, Mathematical and Computer Modelling, 49, 9-10, 1893-1904, (2009) · Zbl 1171.91349
[15] Qian, L.; Wang, W.; Wang, R.; Tang, Y., Valuation of equity-indexed annuity under stochastic mortality and interest rate, Insurance: Mathematics & Economics, 47, 2, 123-129, (2010) · Zbl 1231.91446
[16] Aít-Sahalia, Y., Nonparametric pricing of interest rate derivative securities, Econometrica, 64, 3, 527-560, (1996) · Zbl 0844.62094
[17] Andrew, L., Long-term memory in stock price, Econometrica, 59, 1279-1313, (1991) · Zbl 0781.90023
[18] Granger, C. W. J., A typical spectral shape of an economic variable, Econometrica, 34, 150-161, (1966)
[19] Sottinen, T.; Valkeila, E., Fractional Brownain motion as a model in finance, Report
[20] Willinger, W.; Taqqu, M.; Teverovsky, V., Stock market prices and long-range dependence, Finance and Stochastics, 3, 1-13, (1999) · Zbl 0924.90029
[21] Dudley, R.; Norvaisa, R., An Introduction to P-Variation and Young Integrals with Emphasis on Sample Functions of Stochastic Processes, (1998), MaPhySto, Department of Mathematical Sciences, University of Aarhus · Zbl 0937.28001
[22] Duncan, T. E.; Hu, Y.; Pasik-Duncan, B., Stochastic calculus for fractional Brownian motion. I. Theory, SIAM Journal on Control and Optimization, 38, 2, 582-612, (2000) · Zbl 0947.60061
[23] Hu, Y.; Øksendal, B., Fractional white noise calculus and applications to finance, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6, 1, 1-32, (2003) · Zbl 1045.60072
[24] Norros, I.; Valkeila, E.; Virtamo, J., An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli, 5, 4, 571-587, (1999) · Zbl 0955.60034
[25] Jarrow, R. A.; Protter, P.; Sayit, H., No arbitrage without semimartingales, The Annals of Applied Probability, 19, 2, 596-616, (2009) · Zbl 1172.60027
[26] Soner, H. M.; Shreve, S. E.; Cvitanić, J., There is no nontrivial hedging portfolio for option pricing with transaction costs, The Annals of Applied Probability, 5, 2, 327-355, (1995) · Zbl 0837.90012
[27] Narayan, O., Exact asymptotic queue length distribution for fractional Brownian traffic, Advances in Performance Analysis, 1, 39-63, (1998)
[28] Michna, Z., Self-similar processes in collective risk theory, Journal of Applied Mathematics and Stochastic Analysis, 11, 4, 429-448, (1998) · Zbl 0937.60029
[29] Ferebee, B., An asymptotic expansion for one-sided Brownian exit densities, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 63, 1, 1-15, (1983) · Zbl 0488.60086
[30] Asmussen, S., Ruin Probabilities, (2000), Singapore: World Scientific Publishing, Singapore
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.