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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.
|
[2] |
S. Browne, Stochastic differential portfolio games/em>,, Journal of Applied Probability, 37 (2000), 126.
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. Google Scholar |
[4] |
R. Elliott, The existence of value in stochastic differential games,, SIAM: Journal of Control and Optimizaiton, 14 (1976), 85.
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.
doi: 10.1007/s007800050022. |
[6] |
R. Elliott and P. Kopp, Mathematics of Financial Markets,, $2^{nd}$ edition, (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.
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.
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, (2006).
|
[10] |
X. Guo, Information and option pricings,, Quantitative Finance, 1 (2001), 38.
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.
doi: 10.2307/1912559. |
[12] |
C. Hipp and M. Plum, Optimal investment for insurers,, Insurance: Mathematics and Economics, 27 (2000), 215.
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.
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, (1977).
|
[15] |
H. J. Kusher, Approximations and Weak Convergence Methods for Random Processes,, MIT Press, (1984).
|
[16] |
H. J. Kusher, Numerical methods for stochastic control problems in continuous time,, SIAM: Journal of Control and Optimization, 28 (1990), 990.
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, (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.
|
[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.
doi: 10.3934/jimo.2013.9.487. |
[20] |
S. Pliska, Introduction to Mathematical Finance,, United States: Blackwell Publishing, (1997). Google Scholar |
[21] |
P. E. Protter, Stochastic Integration and Differential Equations,, 2nd edition, (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.
doi: 10.1109/TAC.2007.915169. |
[23] |
S. Wan, Stochastic differential portfolio games based on utility with regime switching model,, in, (2007), 2302.
|
[24] |
H. Yang and L.Zhang, Optimal investment for insurer with jump-diffusion risk process,, Insurance: Mathematics and Economics, 37 (2005), 615.
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.
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.
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.
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.
|
[2] |
S. Browne, Stochastic differential portfolio games/em>,, Journal of Applied Probability, 37 (2000), 126.
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. Google Scholar |
[4] |
R. Elliott, The existence of value in stochastic differential games,, SIAM: Journal of Control and Optimizaiton, 14 (1976), 85.
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.
doi: 10.1007/s007800050022. |
[6] |
R. Elliott and P. Kopp, Mathematics of Financial Markets,, $2^{nd}$ edition, (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.
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.
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, (2006).
|
[10] |
X. Guo, Information and option pricings,, Quantitative Finance, 1 (2001), 38.
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.
doi: 10.2307/1912559. |
[12] |
C. Hipp and M. Plum, Optimal investment for insurers,, Insurance: Mathematics and Economics, 27 (2000), 215.
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.
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, (1977).
|
[15] |
H. J. Kusher, Approximations and Weak Convergence Methods for Random Processes,, MIT Press, (1984).
|
[16] |
H. J. Kusher, Numerical methods for stochastic control problems in continuous time,, SIAM: Journal of Control and Optimization, 28 (1990), 990.
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, (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.
|
[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.
doi: 10.3934/jimo.2013.9.487. |
[20] |
S. Pliska, Introduction to Mathematical Finance,, United States: Blackwell Publishing, (1997). Google Scholar |
[21] |
P. E. Protter, Stochastic Integration and Differential Equations,, 2nd edition, (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.
doi: 10.1109/TAC.2007.915169. |
[23] |
S. Wan, Stochastic differential portfolio games based on utility with regime switching model,, in, (2007), 2302.
|
[24] |
H. Yang and L.Zhang, Optimal investment for insurer with jump-diffusion risk process,, Insurance: Mathematics and Economics, 37 (2005), 615.
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.
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.
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.
doi: 10.3934/jimo.2012.8.673. |
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