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Optimal stochastic investment games under Markov regime switching market
1. | School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui, 241003, China |
2. | School of Finance and Statistics, East China Normal University, Shanghai, 200241 |
3. | School of Finance, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210046, China |
References:
[1] |
S. Browne, Optimal investment policy for a firm with random risk process: Exponential utility and minimizing the probabilty of ruin, Mathematical Operation Research, 20 (1995), 937-958. |
[2] |
S. Browne, Stochastic differential portfolio games/em>, Journal of Applied Probability, 37 (2000), 126-147.
doi: 10.1239/jap/1014842273. |
[3] |
M. Clements and H. Krolzig, Can regime-swichting models reproducing the business cycle features of U.S. aggregate consumption, investment and output? International Journal of Financing and Economics, 9 (2004), 1-14. |
[4] |
R. Elliott, The existence of value in stochastic differential games, SIAM: Journal of Control and Optimizaiton, 14 (1976), 85-94.
doi: 10.1137/0314006. |
[5] |
R. Elliott and J. Hoek, An application of hidden Markov models to asset allocation problems, Finance and Stochastics, 1 (1997), 229-238.
doi: 10.1007/s007800050022. |
[6] |
R. Elliott and P. Kopp, Mathematics of Financial Markets, $2^{nd}$ edition, Springer-Verlag, New York, 2005. |
[7] |
R. Elliott, T. K. Siu and L. Chan, Pricing volatility swaps under Heston's stochastic volatility model with regime switching, Applied Mathematical Finance, 14 (2007), 41-62.
doi: 10.1080/13504860600659222. |
[8] |
W. H. Fleming and P. E. Souganidis, On the existence of value functions of two-player, zero-sum stochastic differential games, Indiana Universtiy Mathematical Journal, 38 (1989), 293-313.
doi: 10.1512/iumj.1989.38.38015. |
[9] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Second edition. Stochastic Modelling and Applied Probability, 25. Springer, New York, 2006. |
[10] |
X. Guo, Information and option pricings, Quantitative Finance, 1 (2001), 38-44.
doi: 10.1080/713665550. |
[11] |
J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.
doi: 10.2307/1912559. |
[12] |
C. Hipp and M. Plum, Optimal investment for insurers, Insurance: Mathematics and Economics, 27 (2000), 215-228.
doi: 10.1016/S0167-6687(00)00049-4. |
[13] |
H. Kushner and S. Chamberlain, On stochastic differential games: Sufficient conditions that a given strategy be a saddle point, and numerical procedures for the solution of the game, Journal of Mathmatical Analysis and Applications, 26 (1969), 560-575.
doi: 10.1016/0022-247X(69)90199-1. |
[14] |
H. J. Kusher, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977. |
[15] |
H. J. Kusher, Approximations and Weak Convergence Methods for Random Processes, MIT Press, Cambirdge, 1984. |
[16] |
H. J. Kusher, Numerical methods for stochastic control problems in continuous time, SIAM: Journal of Control and Optimization, 28 (1990), 990-1048.
doi: 10.1137/0328056. |
[17] |
H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag: New York, 2nd edition, 2001. |
[18] |
H. J. Kushner and S. G. Chamberlain, Finite state stochastic games: existence theorems and computational procedures, IEEE Trans. Automat. Control, 14 (1969), 248-255. |
[19] |
H. Meng, F. Yuen, T. Siu and H. Yang, Optimal portfolio in a continuous-time self-exciting threshold model, Journal of Industrial and Management Optimization, 9 (2013), 487-504.
doi: 10.3934/jimo.2013.9.487. |
[20] |
S. Pliska, Introduction to Mathematical Finance, United States: Blackwell Publishing, 1997. |
[21] |
P. E. Protter, Stochastic Integration and Differential Equations, 2nd edition, Springe-Verlag, 2005. |
[22] |
Q. Song, G. Yin and Z. Zhang, Numercial solutions for stochastic differential games with regime switching, IEEE Transactions on Automatica Control, 53 (2008), 509-521.
doi: 10.1109/TAC.2007.915169. |
[23] |
S. Wan, Stochastic differential portfolio games based on utility with regime switching model, in "2007 IEEE International Conference on Control and Automation, Guangzhou, China", 2007, 2302-2305. |
[24] |
H. Yang and L.Zhang, Optimal investment for insurer with jump-diffusion risk process, Insurance: Mathematics and Economics, 37 (2005), 615-634.
doi: 10.1016/j.insmatheco.2005.06.009. |
[25] |
D. Yao, H. Yang and R. Wang, Optimal financing and dividend strategies in a dual model with proportional costs, Journal of Industrial and Management Optimization, 6 (2010), 761-777.
doi: 10.3934/jimo.2010.6.761. |
[26] |
K. C. Yiu, J. Liu, T. Siu and K., Ching, Optimal portfolios with regime switching and value-at-risk constraint, Automatica, 46 (2010), 979-989.
doi: 10.1016/j.automatica.2010.02.027. |
[27] |
Y. Zeng and Z. Li, Optimal reinsurance-investment strategies for insurers under mean-CaR criteria, Journal of Industrial and Management Optimization, 8 (2012), 673-690.
doi: 10.3934/jimo.2012.8.673. |
show all references
References:
[1] |
S. Browne, Optimal investment policy for a firm with random risk process: Exponential utility and minimizing the probabilty of ruin, Mathematical Operation Research, 20 (1995), 937-958. |
[2] |
S. Browne, Stochastic differential portfolio games/em>, Journal of Applied Probability, 37 (2000), 126-147.
doi: 10.1239/jap/1014842273. |
[3] |
M. Clements and H. Krolzig, Can regime-swichting models reproducing the business cycle features of U.S. aggregate consumption, investment and output? International Journal of Financing and Economics, 9 (2004), 1-14. |
[4] |
R. Elliott, The existence of value in stochastic differential games, SIAM: Journal of Control and Optimizaiton, 14 (1976), 85-94.
doi: 10.1137/0314006. |
[5] |
R. Elliott and J. Hoek, An application of hidden Markov models to asset allocation problems, Finance and Stochastics, 1 (1997), 229-238.
doi: 10.1007/s007800050022. |
[6] |
R. Elliott and P. Kopp, Mathematics of Financial Markets, $2^{nd}$ edition, Springer-Verlag, New York, 2005. |
[7] |
R. Elliott, T. K. Siu and L. Chan, Pricing volatility swaps under Heston's stochastic volatility model with regime switching, Applied Mathematical Finance, 14 (2007), 41-62.
doi: 10.1080/13504860600659222. |
[8] |
W. H. Fleming and P. E. Souganidis, On the existence of value functions of two-player, zero-sum stochastic differential games, Indiana Universtiy Mathematical Journal, 38 (1989), 293-313.
doi: 10.1512/iumj.1989.38.38015. |
[9] |
W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Second edition. Stochastic Modelling and Applied Probability, 25. Springer, New York, 2006. |
[10] |
X. Guo, Information and option pricings, Quantitative Finance, 1 (2001), 38-44.
doi: 10.1080/713665550. |
[11] |
J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.
doi: 10.2307/1912559. |
[12] |
C. Hipp and M. Plum, Optimal investment for insurers, Insurance: Mathematics and Economics, 27 (2000), 215-228.
doi: 10.1016/S0167-6687(00)00049-4. |
[13] |
H. Kushner and S. Chamberlain, On stochastic differential games: Sufficient conditions that a given strategy be a saddle point, and numerical procedures for the solution of the game, Journal of Mathmatical Analysis and Applications, 26 (1969), 560-575.
doi: 10.1016/0022-247X(69)90199-1. |
[14] |
H. J. Kusher, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977. |
[15] |
H. J. Kusher, Approximations and Weak Convergence Methods for Random Processes, MIT Press, Cambirdge, 1984. |
[16] |
H. J. Kusher, Numerical methods for stochastic control problems in continuous time, SIAM: Journal of Control and Optimization, 28 (1990), 990-1048.
doi: 10.1137/0328056. |
[17] |
H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag: New York, 2nd edition, 2001. |
[18] |
H. J. Kushner and S. G. Chamberlain, Finite state stochastic games: existence theorems and computational procedures, IEEE Trans. Automat. Control, 14 (1969), 248-255. |
[19] |
H. Meng, F. Yuen, T. Siu and H. Yang, Optimal portfolio in a continuous-time self-exciting threshold model, Journal of Industrial and Management Optimization, 9 (2013), 487-504.
doi: 10.3934/jimo.2013.9.487. |
[20] |
S. Pliska, Introduction to Mathematical Finance, United States: Blackwell Publishing, 1997. |
[21] |
P. E. Protter, Stochastic Integration and Differential Equations, 2nd edition, Springe-Verlag, 2005. |
[22] |
Q. Song, G. Yin and Z. Zhang, Numercial solutions for stochastic differential games with regime switching, IEEE Transactions on Automatica Control, 53 (2008), 509-521.
doi: 10.1109/TAC.2007.915169. |
[23] |
S. Wan, Stochastic differential portfolio games based on utility with regime switching model, in "2007 IEEE International Conference on Control and Automation, Guangzhou, China", 2007, 2302-2305. |
[24] |
H. Yang and L.Zhang, Optimal investment for insurer with jump-diffusion risk process, Insurance: Mathematics and Economics, 37 (2005), 615-634.
doi: 10.1016/j.insmatheco.2005.06.009. |
[25] |
D. Yao, H. Yang and R. Wang, Optimal financing and dividend strategies in a dual model with proportional costs, Journal of Industrial and Management Optimization, 6 (2010), 761-777.
doi: 10.3934/jimo.2010.6.761. |
[26] |
K. C. Yiu, J. Liu, T. Siu and K., Ching, Optimal portfolios with regime switching and value-at-risk constraint, Automatica, 46 (2010), 979-989.
doi: 10.1016/j.automatica.2010.02.027. |
[27] |
Y. Zeng and Z. Li, Optimal reinsurance-investment strategies for insurers under mean-CaR criteria, Journal of Industrial and Management Optimization, 8 (2012), 673-690.
doi: 10.3934/jimo.2012.8.673. |
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