Discrete sums of geometric Brownian motions, annuities and Asian options
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DOI: 10.1016/j.insmatheco.2016.05.020
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- Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2015. "Geometric stopping of a random walk and its applications to valuing equity-linked death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 313-325.
- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
- Daniel Dufresne, 2007. "Stochastic Life Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(1), pages 136-157.
- N/A, 2007. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 199(1), pages 126-126, January.
- M. Schroder & P. Carr, 2003. "Bessel processes, the integral of geometric Brownian motion, and Asian options," Papers math/0311280, arXiv.org.
- N/A, 2007. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 199(1), pages 126-135, January.
- Vanduffel, Steven & Shang, Zhaoning & Henrard, Luc & Dhaene, Jan & Valdez, Emiliano A., 2008. "Analytic bounds and approximations for annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1109-1117, June.
- Moshe Arye Milevsky & Steven E. Posner, 1999.
"Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma Distribution,"
World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 7, pages 203-218,
World Scientific Publishing Co. Pte. Ltd..
- Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(3), pages 409-422, September.
- Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057, arXiv.org, revised Jan 2016.
- Lingjiong Zhu, 2015. "Options with Extreme Strikes," Risks, MDPI, vol. 3(3), pages 1-16, July.
- Daniel Dufresne, 2007. "Fitting combinations of exponentials to probability distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 23-48, January.
- N/A, 2007. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 200(1), pages 118-127, April.
- Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
- Gjessing, Håkon K. & Paulsen, Jostein, 1997. "Present value distributions with applications to ruin theory and stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 123-144, October.
- Asmussen, Søren & Rojas-Nandayapa, Leonardo, 2008. "Asymptotics of sums of lognormal random variables with Gaussian copula," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2709-2714, November.
- De Schepper, A. & Goovaerts, M. & Delbaen, F., 1992. "The Laplace transform of annuities certain with exponential time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 291-294, December.
- Feng, Runhuan & Volkmer, Hans W., 2012. "Analytical calculation of risk measures for variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 636-648.
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- Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.
- Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
- Dan Pirjol & Lingjiong Zhu, 2020. "Asymptotics of the time-discretized log-normal SABR model: The implied volatility surface," Papers 2001.09850, arXiv.org, revised Mar 2020.
- Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.
- Brignone, Riccardo & Kyriakou, Ioannis & Fusai, Gianluca, 2021. "Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 232-247.
- Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
- Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
- Zadourian, Rubina & Klümper, Andreas, 2018. "Exact probability distribution function for the volatility of cumulative production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 59-66.
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Keywords
Sum of geometric Brownian motions; Stochastic recurrence equations; Geometric stopping; Annuities; Asian options; Exponential Lévy processes;All these keywords.
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