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An optimal mean-reversion trading rule under a Markov chain model
1. | Department of Mathematics, University of Georgia, Athens, GA 30602, United States, United States |
References:
[1] |
B. R. Barmish and J. A. Primbs, On market-neutral stock trading arbitrage via linear feedback, Proc. American Control Conference, Montreal, (2012), 3693-3698.
doi: 10.1109/ACC.2012.6315392. |
[2] |
C. Blanco and D. Soronow, Mean reverting processes - Energy price processes used for derivatives pricing and risk management, Commodities Now, 5 (2001), 68-72. |
[3] |
L. P. Bos, A. F. Ware and B. S. Pavlov, On a semi-spectral method for pricing an option on a mean-reverting asset, Quantitative Finance, 2 (2002), 337-345.
doi: 10.1088/1469-7688/2/5/302. |
[4] |
T. J. I'A. Bromwich, An introduction to the Theory of Infinite Series, American Mathematical Society, AMS Chelsea Publishing, Providence, RI, 1991. |
[5] |
A. Cowles and H. Jones, Some posteriori probabilities in stock market action, Econometrica, 5 (1937), 280-294.
doi: 10.2307/1905515. |
[6] |
J. Cox, J. Ingersoll and S. Ross, A theory of the term structure of interest rates, Econometrica, 53 (1985), 385-407.
doi: 10.2307/1911242. |
[7] |
M. Dai, Q. Zhang and Q. Zhu, Trend following trading under a regime switching model, SIAM Journal on Financial Mathematics, 1 (2010), 780-810.
doi: 10.1137/090770552. |
[8] |
R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Second edition. Springer Finance. Springer-Verlag, New York, 2005. |
[9] |
E. Fama and K. R. French, Permanent and temporary components of stock prices, J. Political Economy, 96 (1988), 246-273.
doi: 10.1086/261535. |
[10] |
J. P. Fouque, G. Papanicolaou and R. K. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, 2000. |
[11] |
L. A. Gallagher and M. P. Taylor, Permanent and temporary components of stock prices: Evidence from assessing macroeconomic shocks, Southern Economic Journal, 69 (2002), 345-362.
doi: 10.2307/1061676. |
[12] |
E. Gatev, W. N. Goetzmann and K. G. Rouwenhorst, Pairs trading: Performance of a relative-value arbitrage rule, Review of Financial Studies, 19 (2006), 797-827. |
[13] |
X. Guo and Q. Zhang, Optimal selling rules in a regime switching model, IEEE Trans. Automatic Control, 50 (2005), 1450-1455.
doi: 10.1109/TAC.2005.854657. |
[14] |
C. M. Hafner and H. Herwartz, Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis, J. Empirical Finance, 8 (2001), 1-34.
doi: 10.1016/S0927-5398(00)00024-4. |
[15] |
J. C. Hull, Options, Futures, and Other Derivatives, 3rd Ed., Prentice Hall, Upper Saddle River, NJ, 1997. |
[16] |
S. Iwarere and B. R. Barmish, A confidence interval triggering method for stock trading via feedback control, Proc. American Control Conference, Baltimore, MD, (2010), 6910-6916.
doi: 10.1109/ACC.2010.5531311. |
[17] |
I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, Springer, New York, 1998.
doi: 10.1007/b98840. |
[18] |
A. Merhi and M. Zervos, A model for reversible investment capacity expansion, SIAM J. Control Optim., 46 (2007), 839-876.
doi: 10.1137/050640758. |
[19] |
W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd Edition, Springer-Verlag, Berlin $\cdot$ Heidelberg $\cdot$ GmbH, 1966. |
[20] |
M. Musiela and M. Rutkowski, Martingale Methods in Financial Modeling, Springer, New York, 1997.
doi: 10.1007/978-3-662-22132-7. |
[21] |
R. Norberg, The Markov chain market, ASTIN Bulletin, 33 (2003), 265-287.
doi: 10.2143/AST.33.2.503693. |
[22] |
Q. S. Song and Q. Zhang, An optimal pairs-trading rule, Automatica, 49 (2013), 3007-3014.
doi: 10.1016/j.automatica.2013.07.012. |
[23] |
J. Van der Hoek and R. J. Elliott, American option prices in a Markov chain market model, Applied Stochastic Models in Business and Industry, 28 (2012), 35-59.
doi: 10.1002/asmb.893. |
[24] |
O. A. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics, 5 (1977), 177-188. |
[25] |
Z. X. Wang and D. R. Guo, Special Functions, World Scientific Publishing Co Pte Ltd, Singapore, 1989.
doi: 10.1142/0653. |
[26] |
G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications, A Two-Time-Scale Approach, 2nd Ed, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4346-9. |
[27] |
H. Zhang and Q. Zhang, Trading a mean-reverting asset: Buy low and sell high, Automatica, 44 (2008), 1511-1518.
doi: 10.1016/j.automatica.2007.11.003. |
[28] |
Q. Zhang, Stock trading: An optimal selling rule, SIAM J. Control Optim., 40 (2001), 64-87.
doi: 10.1137/S0363012999356325. |
[29] |
Q. Zhang, Explicit solutions for an optimal stock selling problem under a Markov chain model, J. Mathematical Analysis and Applications, 420 (2014), 1210-1227.
doi: 10.1016/j.jmaa.2014.06.049. |
show all references
References:
[1] |
B. R. Barmish and J. A. Primbs, On market-neutral stock trading arbitrage via linear feedback, Proc. American Control Conference, Montreal, (2012), 3693-3698.
doi: 10.1109/ACC.2012.6315392. |
[2] |
C. Blanco and D. Soronow, Mean reverting processes - Energy price processes used for derivatives pricing and risk management, Commodities Now, 5 (2001), 68-72. |
[3] |
L. P. Bos, A. F. Ware and B. S. Pavlov, On a semi-spectral method for pricing an option on a mean-reverting asset, Quantitative Finance, 2 (2002), 337-345.
doi: 10.1088/1469-7688/2/5/302. |
[4] |
T. J. I'A. Bromwich, An introduction to the Theory of Infinite Series, American Mathematical Society, AMS Chelsea Publishing, Providence, RI, 1991. |
[5] |
A. Cowles and H. Jones, Some posteriori probabilities in stock market action, Econometrica, 5 (1937), 280-294.
doi: 10.2307/1905515. |
[6] |
J. Cox, J. Ingersoll and S. Ross, A theory of the term structure of interest rates, Econometrica, 53 (1985), 385-407.
doi: 10.2307/1911242. |
[7] |
M. Dai, Q. Zhang and Q. Zhu, Trend following trading under a regime switching model, SIAM Journal on Financial Mathematics, 1 (2010), 780-810.
doi: 10.1137/090770552. |
[8] |
R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Second edition. Springer Finance. Springer-Verlag, New York, 2005. |
[9] |
E. Fama and K. R. French, Permanent and temporary components of stock prices, J. Political Economy, 96 (1988), 246-273.
doi: 10.1086/261535. |
[10] |
J. P. Fouque, G. Papanicolaou and R. K. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, 2000. |
[11] |
L. A. Gallagher and M. P. Taylor, Permanent and temporary components of stock prices: Evidence from assessing macroeconomic shocks, Southern Economic Journal, 69 (2002), 345-362.
doi: 10.2307/1061676. |
[12] |
E. Gatev, W. N. Goetzmann and K. G. Rouwenhorst, Pairs trading: Performance of a relative-value arbitrage rule, Review of Financial Studies, 19 (2006), 797-827. |
[13] |
X. Guo and Q. Zhang, Optimal selling rules in a regime switching model, IEEE Trans. Automatic Control, 50 (2005), 1450-1455.
doi: 10.1109/TAC.2005.854657. |
[14] |
C. M. Hafner and H. Herwartz, Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis, J. Empirical Finance, 8 (2001), 1-34.
doi: 10.1016/S0927-5398(00)00024-4. |
[15] |
J. C. Hull, Options, Futures, and Other Derivatives, 3rd Ed., Prentice Hall, Upper Saddle River, NJ, 1997. |
[16] |
S. Iwarere and B. R. Barmish, A confidence interval triggering method for stock trading via feedback control, Proc. American Control Conference, Baltimore, MD, (2010), 6910-6916.
doi: 10.1109/ACC.2010.5531311. |
[17] |
I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, Springer, New York, 1998.
doi: 10.1007/b98840. |
[18] |
A. Merhi and M. Zervos, A model for reversible investment capacity expansion, SIAM J. Control Optim., 46 (2007), 839-876.
doi: 10.1137/050640758. |
[19] |
W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd Edition, Springer-Verlag, Berlin $\cdot$ Heidelberg $\cdot$ GmbH, 1966. |
[20] |
M. Musiela and M. Rutkowski, Martingale Methods in Financial Modeling, Springer, New York, 1997.
doi: 10.1007/978-3-662-22132-7. |
[21] |
R. Norberg, The Markov chain market, ASTIN Bulletin, 33 (2003), 265-287.
doi: 10.2143/AST.33.2.503693. |
[22] |
Q. S. Song and Q. Zhang, An optimal pairs-trading rule, Automatica, 49 (2013), 3007-3014.
doi: 10.1016/j.automatica.2013.07.012. |
[23] |
J. Van der Hoek and R. J. Elliott, American option prices in a Markov chain market model, Applied Stochastic Models in Business and Industry, 28 (2012), 35-59.
doi: 10.1002/asmb.893. |
[24] |
O. A. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics, 5 (1977), 177-188. |
[25] |
Z. X. Wang and D. R. Guo, Special Functions, World Scientific Publishing Co Pte Ltd, Singapore, 1989.
doi: 10.1142/0653. |
[26] |
G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications, A Two-Time-Scale Approach, 2nd Ed, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4346-9. |
[27] |
H. Zhang and Q. Zhang, Trading a mean-reverting asset: Buy low and sell high, Automatica, 44 (2008), 1511-1518.
doi: 10.1016/j.automatica.2007.11.003. |
[28] |
Q. Zhang, Stock trading: An optimal selling rule, SIAM J. Control Optim., 40 (2001), 64-87.
doi: 10.1137/S0363012999356325. |
[29] |
Q. Zhang, Explicit solutions for an optimal stock selling problem under a Markov chain model, J. Mathematical Analysis and Applications, 420 (2014), 1210-1227.
doi: 10.1016/j.jmaa.2014.06.049. |
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