Optimal stopping behavior of equity-linked investment products with regime switching. (English) Zbl 1129.60065

Summary: In recent years, there is a growing interest in equity-linked investment products. The return credited to such product depends on the return of some underlying reference index. A prominent example is the equity-indexed annuities (EIAs). A special feature of many of the equity-linked products is that the holders are entitled the right to surrender the product prior to maturity. In this paper, we will study the optimal surrender time for a equity-linked product in a discrete-time setting. We assume that the market environment will switch among different regimes in a Markovian way, and the return of the reference index will have different distributions in different regimes. Assuming a CRRA preference, we have obtained the optimal surrender policy. Properties of the optimal surrender behavior, in particular the effect of regime switching, are examined.


60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G40 Stopping times; optimal stopping problems; gambling theory
91B28 Finance etc. (MSC2000)
Full Text: DOI


[1] Aase, K.K.; Persson, S.A., Pricing of unit-linked life insurance policies, Scandinavian actuarial journal, 1, 26-52, (1994) · Zbl 0814.62067
[2] Altieri, A.; Vargiolu, T., Optimal default boundary in a discrete time setting, () · Zbl 0976.91042
[3] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 81, 637-659, (1973) · Zbl 1092.91524
[4] Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Actuarial mathematics, (1997), The Society of Actuaries Illinois · Zbl 0634.62107
[5] Brennan, M.J.; Schwartz, E.S., The pricing of equity-linked life insurance policies with an asset value guarantee, Journal of financial economics, 3, 195-213, (1976)
[6] Buffington, J.; Elliott, R.J., American options with regime switching, International journal of theoretical and applied finance, 5, 497-514, (2002) · Zbl 1107.91325
[7] Campbell, J.Y.; Viceira, L.M., Strategic asset allocation: portfolio choice for long-term investors, (2001), Oxford University Press New York
[8] Cheung, K.C.; Yang, H., Asset allocation with regime-switching: discrete-time case, ASTIN bulletin, 34, 247-257, (2004)
[9] Cheung, K.C., Yang, H., 2005. Optimal consumption strategy in a discrete-time model with credit risk, submitted for publication.
[10] Di Masi, G.B.; Kabanov, Y.M.; Runggaldier, W.J., Mean variance hedging of options on stocks with Markov volatility, Theory of probability and applications, 39, 173-181, (1994) · Zbl 0836.60075
[11] Embrechts, P., Actuarial versus financial pricing of insurance, Risk finance, 1, 17-26, (2000)
[12] Embrechts, P.; Samorodnitsky, G., Ruin problem, operational risk and how fast stochastic processes mix, The annals of applied probability, 13, 1-36, (2003) · Zbl 1022.60018
[13] Gerber, H.U.; Pafuni, G., Pricing dynamic investment fund protection, North American actuarial journal, 4, 28-37, (2001)
[14] Gerber, H.U.; Shiu, E.S.W., Pricing perpetual fund protection with withdraw option, North American actuarial journal, 7, 60-77, (2003)
[15] Hamilton, J., A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57, 357-384, (1989) · Zbl 0685.62092
[16] Hardy, M.R., A regime-switching model of long-term stock returns, North American actuarial journal, 5, 41-53, (2001) · Zbl 1083.62530
[17] Hardy, M.R., Investment guarantees: the new science of modeling and risk management for equity-linked insurance, (2003), John Wiley New York · Zbl 1092.91042
[18] Huang, C.F.; Litzenberger, R.H., Foundations for financial economics, (1988), Prentice Hall New Jersey · Zbl 0677.90001
[19] Korn, R., Optimal portfolios: stochastic models for optimal investment and risk management in continuous time, (1997), World Scientific Singapore · Zbl 0931.91017
[20] Merton, R.C., Lifetime portfolio selection under uncertainty: the continuous-time case, Review of economics and statistics, 51, 247-257, (1969)
[21] Merton, R.C., The theory of rational option pricing, Bell journal of economics and management science, 4, 141-183, (1973) · Zbl 1257.91043
[22] Moore, K.S.; Young, V.R., Optimal design of a perpetual equity-indexed annuity, North American actuarial journal, 9, 57-72, (2005) · Zbl 1085.60512
[23] Müller, A.; Stoyan, D., Comparison methods for stochastic models and risks, (2002), John Wiley and Sons · Zbl 0999.60002
[24] Neveu, J., Discrete-parameter martingakes, (1975), North-Holland Amsterdam-Oxford
[25] Norberg, R., The Markov chain markets, ASTIN bulletin, 33, 265-287, (2003) · Zbl 1098.91531
[26] Rolski, T.; Schmidli, H.; Schmidt, V.; Teugels, J., Stochastic processes for insurance and finance, (1999), John Wiley and Sons · Zbl 0940.60005
[27] Samuelson, P.A., Lifetime portfolio selection by dynamic stochastic programming, The review of economics and statistics, 51, 239-246, (1969)
[28] Shaked, M.; Shanthikumar, J.G., Stochastic orders and their applications, (1994), Academic Press · Zbl 0806.62009
[29] Shiryaev, A.N., Statistical sequential analysis, (1973), American Mathematical Society · Zbl 0267.62039
[30] Tiong, S., Valuing equity-indexed annuities, North American actuarial journal, 4, 149-163, (2000) · Zbl 1083.62545
[31] Yin, G.; Zhou, X.Y., Markowitz’s mean – variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits, IEEE transactions on automatic control, 49, 349-360, (2003) · Zbl 1366.91148
[32] Zariphopoulou, T., Investment – consumption models with transactions costs and Markov-chain parameters, SIAM journal on control and optimization, 30, 613-636, (1992) · Zbl 0784.90027
[33] Zhang, Q., Stock trading: an optimal selling rule, SIAM journal on control and optimization, 40, 64-87, (2001) · Zbl 0990.91014
[34] Zhou, X.Y.; Yin, G., Markowitz’s mean – variance portfolio selection with regime switching: a continuous-time model, SIAM journal on control and optimization, 42, 1466-1482, (2003) · Zbl 1175.91169
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