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Optimal stochastic differential games with VaR constraints
1. | School of Insurance, Central University Of Finance and Economics, Beijing 100081, China |
2. | Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
References:
[1] |
N. U. Ahmed and K. L. Teo, "Optimal Control of Distributed Parameter Systems," North Holland, 1981. |
[2] |
L. Bai and J. Guo, Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint, Insurance Math. Econom., 42 (2008), 968-975.
doi: 10.1016/j.insmatheco.2007.11.002. |
[3] |
N. Bauerle, Benchmark and mean-variance problems for insurers, Mathematical Methods of Operations Research, 62 (2005), 159-165.
doi: 10.1007/s00186-005-0446-1. |
[4] |
R. Bingham, Risk and return: Underwriting, investment and leverage probability of surplus drawdown and pricing for underwriting and investment risk, in "Proceedings of the Casualty Actuarial Society Casualty Actuarial Society," (Arlington, Virginia, 2000), LXXXVII, 31-78. |
[5] |
S. Bouma, "Risk Management in the Insurance Industry and Solvency II," European Survey, Capgemini, November 7, 2006. |
[6] |
S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 20 (1995), 937-958.
doi: 10.1287/moor.20.4.937. |
[7] |
S. Browne, Stochastic differential portfolio games, J. Appl. Prob., 37 (2000), 126-147.
doi: 10.1239/jap/1014842273. |
[8] |
R. J. Elliott and T. K. Siu, On risk minimizing portfolio choice under Markovian regime-switching model, Ann. Oper. Res., 176 (2010), 271-291.
doi: 10.1007/s10479-008-0448-5. |
[9] |
R. J. Elliott and T. K. Siu, A stochastic differential game for optimal investment of an insurer with regime switching, Quant. Finance, 11 (2011), 365-380.
doi: 10.1080/14697681003591704. |
[10] |
B. Højgaard and M. Taksar, Optimal proportional reinsurance policies for diffusion models, Scand. Actuar. J., 22 (1998), 166-180. |
[11] |
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a value-at-risk constraint, Journal of Industrial and Management Optimization, 8 (2012), 531-547.
doi: 10.3934/jimo.2012.8.531. |
[12] |
J. Z. Liu, K. F. C. Yiu and K. L. Teo, Optimal Portfolios with stress analysis and the effect of a CVaR constraint, Pac. J. Optim., 7 (2011), 83-95. |
[13] |
S. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance Math. Econom., 42 (2008), 434-444.
doi: 10.1016/j.insmatheco.2007.04.002. |
[14] |
B. Øksendal and A. Sulem, "A Game Theoretic Approach to Amrtingale Measures in Incomplete Markets," University of Oslo and INRIA, 2006. |
[15] |
D. S. Promislow and V. R. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109-128. |
[16] |
H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scand. Actuar. J., 2001 (2001), 55-68.
doi: 10.1080/034612301750077338. |
[17] |
H. Schmidli, On minimizing the ruin probability by investment and reinsurance, Ann. Appl. Probab., 12 (2002), 890-907.
doi: 10.1214/aoap/1031863173. |
[18] |
J. Suijs, A. De Waegenaere and P. Borm, Stochastic cooperative games in insurance, Insurance Math. Econom., 22 (1998), 209-228.
doi: 10.1016/S0167-6687(97)00038-3. |
[19] |
K. L. Teo, D. W. Reid and I. E. Boyd, Stochastic optimal control theory and its computational method, Internat. J. Systems Sci., 11 (1980), 77-95.
doi: 10.1080/00207728008966998. |
[20] |
H. Yang and L. Zhang, Optimal investment for insurer with jump-diffusion risk process, Insurance Math. Econom., 37 (2005), 615-634.
doi: 10.1016/j.insmatheco.2005.06.009. |
[21] |
K. F. C. Yiu, Optimal portfolio under a value-at-risk constraint, J. Econom. Dynam. Control, 28 (2004), 1317-1334.
doi: 10.1016/S0165-1889(03)00116-7. |
[22] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 979-989.
doi: 10.1016/j.automatica.2010.02.027. |
[23] |
X. D. Zeng, A stochastic differential reinsurance game, J. Appl. Prob., 47 (2010), 335-349.
doi: 10.1239/jap/1276784895. |
[24] |
X. Zhang and T. K. Siu, Optimal investment and reinsurance of an insurer with model uncertainty, Insurance Math. Econom., 45 (2009), 81-88.
doi: 10.1016/j.insmatheco.2009.04.001. |
show all references
References:
[1] |
N. U. Ahmed and K. L. Teo, "Optimal Control of Distributed Parameter Systems," North Holland, 1981. |
[2] |
L. Bai and J. Guo, Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint, Insurance Math. Econom., 42 (2008), 968-975.
doi: 10.1016/j.insmatheco.2007.11.002. |
[3] |
N. Bauerle, Benchmark and mean-variance problems for insurers, Mathematical Methods of Operations Research, 62 (2005), 159-165.
doi: 10.1007/s00186-005-0446-1. |
[4] |
R. Bingham, Risk and return: Underwriting, investment and leverage probability of surplus drawdown and pricing for underwriting and investment risk, in "Proceedings of the Casualty Actuarial Society Casualty Actuarial Society," (Arlington, Virginia, 2000), LXXXVII, 31-78. |
[5] |
S. Bouma, "Risk Management in the Insurance Industry and Solvency II," European Survey, Capgemini, November 7, 2006. |
[6] |
S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 20 (1995), 937-958.
doi: 10.1287/moor.20.4.937. |
[7] |
S. Browne, Stochastic differential portfolio games, J. Appl. Prob., 37 (2000), 126-147.
doi: 10.1239/jap/1014842273. |
[8] |
R. J. Elliott and T. K. Siu, On risk minimizing portfolio choice under Markovian regime-switching model, Ann. Oper. Res., 176 (2010), 271-291.
doi: 10.1007/s10479-008-0448-5. |
[9] |
R. J. Elliott and T. K. Siu, A stochastic differential game for optimal investment of an insurer with regime switching, Quant. Finance, 11 (2011), 365-380.
doi: 10.1080/14697681003591704. |
[10] |
B. Højgaard and M. Taksar, Optimal proportional reinsurance policies for diffusion models, Scand. Actuar. J., 22 (1998), 166-180. |
[11] |
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a value-at-risk constraint, Journal of Industrial and Management Optimization, 8 (2012), 531-547.
doi: 10.3934/jimo.2012.8.531. |
[12] |
J. Z. Liu, K. F. C. Yiu and K. L. Teo, Optimal Portfolios with stress analysis and the effect of a CVaR constraint, Pac. J. Optim., 7 (2011), 83-95. |
[13] |
S. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance Math. Econom., 42 (2008), 434-444.
doi: 10.1016/j.insmatheco.2007.04.002. |
[14] |
B. Øksendal and A. Sulem, "A Game Theoretic Approach to Amrtingale Measures in Incomplete Markets," University of Oslo and INRIA, 2006. |
[15] |
D. S. Promislow and V. R. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109-128. |
[16] |
H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scand. Actuar. J., 2001 (2001), 55-68.
doi: 10.1080/034612301750077338. |
[17] |
H. Schmidli, On minimizing the ruin probability by investment and reinsurance, Ann. Appl. Probab., 12 (2002), 890-907.
doi: 10.1214/aoap/1031863173. |
[18] |
J. Suijs, A. De Waegenaere and P. Borm, Stochastic cooperative games in insurance, Insurance Math. Econom., 22 (1998), 209-228.
doi: 10.1016/S0167-6687(97)00038-3. |
[19] |
K. L. Teo, D. W. Reid and I. E. Boyd, Stochastic optimal control theory and its computational method, Internat. J. Systems Sci., 11 (1980), 77-95.
doi: 10.1080/00207728008966998. |
[20] |
H. Yang and L. Zhang, Optimal investment for insurer with jump-diffusion risk process, Insurance Math. Econom., 37 (2005), 615-634.
doi: 10.1016/j.insmatheco.2005.06.009. |
[21] |
K. F. C. Yiu, Optimal portfolio under a value-at-risk constraint, J. Econom. Dynam. Control, 28 (2004), 1317-1334.
doi: 10.1016/S0165-1889(03)00116-7. |
[22] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 979-989.
doi: 10.1016/j.automatica.2010.02.027. |
[23] |
X. D. Zeng, A stochastic differential reinsurance game, J. Appl. Prob., 47 (2010), 335-349.
doi: 10.1239/jap/1276784895. |
[24] |
X. Zhang and T. K. Siu, Optimal investment and reinsurance of an insurer with model uncertainty, Insurance Math. Econom., 45 (2009), 81-88.
doi: 10.1016/j.insmatheco.2009.04.001. |
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