×

zbMATH — the first resource for mathematics

Risk-minimizing hedging strategy for an equity-indexed annuity under a regime switching model. (English) Zbl 1326.60111
Summary: The equity-indexed annuity (EIA) contract offers a proportional participation in the performance of a specified equity index, in addition to a guaranteed return on the single premium. How to manage the risk of the EIA is an important issue. This paper considers the hedging of the EIA. We assume that the parameters of the financial model depend on a continuous-time finite-state Markov chain and the Markov chain is observed, that is the Markov regime switching model. The state of the Markov chain can be interpreted as the state of an economy. Under the regime switching model, we obtain the risk-minimizing hedging strategy for the EIA.
MSC:
60J28 Applications of continuous-time Markov processes on discrete state spaces
60J27 Continuous-time Markov processes on discrete state spaces
91B30 Risk theory, insurance (MSC2010)
91G80 Financial applications of other theories
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Boyle, P; Tian, W, The design of equity-indexed annuities, Insurance: Mathematics and Economics, 43, 303-315, (2008) · Zbl 1152.91484
[2] Chan, T, Pricing contingent claims on stocks driven by Lévy processes, The Annals of Applied Probability, 9, 504-528, (1999) · Zbl 1054.91033
[3] Deshpande, A; Ghosh, MK, Risk minimizing option pricing in a regime switching market, Stochastic Analysis and Applications, 26, 313-324, (2008) · Zbl 1133.91415
[4] Elliott, RJ; Chan, L; Siu, TK, Option pricing and esscher transform under regime switching, Annals of fianance, 1, 423-432, (2005) · Zbl 1233.91270
[5] Föllmer, H; Schweizer, M; Davis, M (ed.); Elliot, R (ed.), Hedging of contingent claims under incomplete information, No. 5, 389-414, (1991) · Zbl 0738.90007
[6] Föllmer, H; Sondermann, D; Hildenbrand, W (ed.); Mas-Colell, A (ed.), Hedging of non-redundant contingent claims, 205-223, (1986), North-Holland
[7] Gerber, HU; Shiu, ESW, Pricing lookback options and dynamic guarantees, North American Actuarial Journal, 47, 48-67, (2003) · Zbl 1084.91507
[8] Ghosh, MK; Arapostathis, A; Marcus, SI, Ergodic control of switching diffusions, SIAM Journal of Contral and Optimization, 35, 1952-1988, (1997) · Zbl 0891.93081
[9] Hamilton, JD, A new approach to the economic analysis of nonstationary time series and the business cycle, Ecomometrica, 57, 357-384, (1989) · Zbl 0685.62092
[10] Hardy, M. Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance. John Wiley & Sons, Inc., Ontario, Canada, 2003 · Zbl 1092.91042
[11] Hardy, M, Ratchet equity indexed annuities, (2004)
[12] Jaimungal, S. Pricing and hedging equity indexed annuities with variance gamma deviates. Working Paper, Department of Statistics, University of Toronto, 2004
[13] Kijima, M; Wong, T, Pricing of ratchet equity-indexed annuities under stochastic interest rates, Insurance: Mathematics and Economics, 41, 317-338, (2007) · Zbl 1141.91457
[14] Lee, H, Pricing equity-indexed annuities with path-dependent options, Insurance: Mathematics and Economics, 33, 677-690, (2003) · Zbl 1103.91368
[15] Lin, XD; Tan, KS, Valuation of equity-indexed annuities under stochastic interest rates, North American Actuarial Journal, 7, 72-91, (2003) · Zbl 1084.60530
[16] Moore, KS, Optimal surrender strategies for equity-indexed annuity investors, Insurance: Mathematics and Economics, 44, 1-18, (2009) · Zbl 1156.91379
[17] Møller, T, Risk-minimizing hedging strategies for unit-linked life insurance contracts, ASTIN Bulletin, 28, 17-47, (1998) · Zbl 1168.91417
[18] Møller, T, Risk-mimizing hedging strategies for insurance payment processes, Finance and Stochastics, 5, 419-446, (2001) · Zbl 0983.62076
[19] Riesner, M, Hedging life insurance contracts in a Lévy process financial market, Insurance: Mathematics and Economics, 38, 599-608, (2006) · Zbl 1168.91419
[20] Schweizer, M, Option hedging for semimartingales, Stochastic Processes and their Applications, 37, 339-363, (1991) · Zbl 0735.90028
[21] Schweizer, M, Risk-minimizing hedging strategies under restricted information, Mathematical Finance, 4, 327-342, (1994) · Zbl 0884.90051
[22] Schweizer, M. A Guided Tour through Quadratic Hedging Approaches. Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management. Cambridge University Press, Cambridge, 538-574, 2001 · Zbl 0992.91036
[23] Tiong, S, Valuing equity indexed annuities, North American Actuarial Journal, 4, 149-163, (2000) · Zbl 1083.62545
[24] Vandaele, N; Vanmaele, M, A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market, Insurance: Mathematics and Economics, 42, 1128-1137, (2008) · Zbl 1141.91549
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.