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Pricing dynamic fund protections with regime switching. (English) Zbl 1329.91130

Summary: This paper deals with the valuation of dynamic fund protections in a Markov regime-switching environment. The volatility switches over time subject to a continuous-time Markov chain. Using a regime-switching diffusion process to describe the primary mutual fund value, explicit solutions of the Laplace transforms of the value of the dynamic fund protection are obtained through martingale technique. Moreover, we analyze the value of dynamic fund protections under a generalized regime-switching jump diffusion model. Due to the complexity of Markov regime-switching, the jump process involved, and the nonlinearity, closed-form formulas for dynamic fund protection prices are virtually impossible to obtain. We design a numerical algorithm according to the Markov chain approximation techniques and obtain numerical results of the value of dynamic fund protection.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B30 Risk theory, insurance (MSC2010)
62M02 Markov processes: hypothesis testing
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[1] Gerber, H. U.; Shiu, E. S., Pricing perpetual options for jump processes, N. Am. Actuar. J., 2, 3, 101-107, (1998) · Zbl 1081.91528
[2] Gerber, H. U.; Shiu, E. S., From ruin theory to pricing reset guarantees and perpetual put options, Insurance Math. Econom., 24, 1, 3-14, (1999) · Zbl 0939.91065
[3] Gerber, H. U.; Pafumi, G., Pricing dynamic investment fund protection, N. Am. Actuar. J., 4, 2, 28-37, (2000) · Zbl 1083.91516
[4] Imai, J.; Boyle, P. P., Dynamic fund protection, N. Am. Actuar. J., 5, 3, 31-47, (2001) · Zbl 1083.60513
[5] Gerber, H. U.; Shiu, E. S., Pricing lookback options and dynamic guarantees, N. Am. Actuar. J., 7, 1, 48-66, (2003) · Zbl 1084.91507
[6] Gerber, H. U.; Shiu, E. S., Pricing perpetual fund protection with withdrawal option, N. Am. Actuar. J., 7, 2, 60-77, (2003) · Zbl 1084.60512
[7] Chu, C. C.; Kwok, Y. K., Reset and withdrawal rights in dynamic fund protection, Insurance Math. Econom., 34, 2, 273-295, (2004) · Zbl 1136.91421
[8] Tse, W. M.; Chang, E. C.; Li, L. K.; Mok, H. M., Pricing and hedging of discrete dynamic guaranteed funds, J. Risk Insurance, 75, 1, 167-192, (2008)
[9] Fung, H. K.; Li, L. K., Pricing discrete dynamic fund protections, N. Am. Actuar. J., 7, 4, 23-31, (2003) · Zbl 1084.91506
[10] Wong, H. Y., Analytical valuation of dynamic fund protection under CEV, WSEAS Trans. Math., 6, 2, 324-329, (2007)
[11] Wong, H. Y.; Chan, C. M., Lookback options and dynamic fund protection under multiscale stochastic volatility, Insurance Math. Econom., 40, 3, 357-385, (2007) · Zbl 1183.91173
[12] Ang, A.; Bekaert, G., International asset allocation with regime shifts, Rev. Financ. Stud., 15, 4, 1137-1187, (2002)
[13] Kou, S. G.; Wang, H., First passage times of a jump diffusion process, Adv. Appl. Probab., 35, 504-531, (2003) · Zbl 1037.60073
[14] Kou, S. G.; Wang, H., Option pricing under a double exponential jump diffusion model, Manage. Sci., 50, 9, 1178-1192, (2004)
[15] Cai, N.; Kou, S. G., Option pricing under a mixed-exponential jump diffusion model, Manage. Sci., 57, 11, 2067-2081, (2011)
[16] Wong, H. Y.; Lam, K. W., Valuation of discrete dynamic fund protection under Lévy processes, N. Am. Actuar. J., 13, 2, 202-216, (2009)
[17] Siu, C. C.; Yam, S. C.P.; Yang, H., Valuing equity-linked death benefits in a regime-switching framework, ASTIN Bull., 45, 02, 355-395, (2015) · Zbl 1390.91211
[18] Gerber, H. U.; Landry, B., On the discounted penalty at ruin in a jump-diffusion and the perpetual put option, Insurance Math. Econom., 22, 3, 263-276, (1998) · Zbl 0924.60075
[19] Sato, K., Lévy processes and infinitely divisible distributions, (1999), Cambridge University Press · Zbl 0973.60001
[20] Bernyk, V.; Dalang, R. C.; Peskir, G., The law of the supremum of a stable Lévy process with no negative jumps, Ann. Probab., 1777-1789, (2008) · Zbl 1185.60051
[21] Jin, Z.; Yang, H.; Yin, G., Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections, Automatica, 49, 8, 2317-2329, (2013) · Zbl 1364.93863
[22] Gerber, H. U.; Shiu, E. S.; Yang, H., Valuing equity-linked death benefits and other contingent options: a discounted density approach, Insurance Math. Econom., 51, 1, 73-92, (2012) · Zbl 1284.91233
[23] Gerber, H. U.; Shiu, E. S.; Yang, H., Valuing equity-linked death benefits in jump diffusion models, Insurance Math. Econom., 53, 3, 615-623, (2013) · Zbl 1290.91162
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