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Optimal switching at Poisson random intervention times
1. | Department of Mathematics, King's College London, Strand, London, WC2R 2LS, United Kingdom |
2. | Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, United Kingdom |
References:
[1] |
E. Bayraktar and M. Egami, On the one-dimensional optimal switching problem, Mathematics of Operations Research, 35 (2010), 140-159.
doi: 10.1287/moor.1090.0432. |
[2] |
E. Bayraktar and M. Ludkovski, A sequential tracking of a hidden Markov chain using point process observations, Stochastic Processes and Their Applications, 119 (2009), 1792-1822.
doi: 10.1016/j.spa.2008.09.003. |
[3] |
A. Bensoussan and J. L. Lions, Impulse Control and Quasivariational Inequalities, Gauthier-Villars, Paris, 1984. |
[4] |
K. Brekke and B. Oksendal, Optimal switching in an economic activity under uncertainty, SIAM J. Control Optim., 32 (1994), 1021-1036.
doi: 10.1137/S0363012992229835. |
[5] |
P. Briand and H. Ying, Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs, Journal of Functional Analysis, 155 (1998), 455-494.
doi: 10.1006/jfan.1997.3229. |
[6] |
R. Carmona and M. Ludkovski, Pricing asset scheduling flexibility using optimal switching, Applied Mathematical Finance, 15 (2008), 405-447.
doi: 10.1080/13504860802170507. |
[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. W. R. Darling and E. Pardoux, Backwards SDE with random terminal time and applications to semilinear elliptic PDE, The Annals of Probability, 25 (1997), 1135-1159.
doi: 10.1214/aop/1024404508. |
[9] |
K. Duckworth and M. Zervos, A model for investment decisions with switching costs, The Annals of Applied probability, 11 (2001), 239-260.
doi: 10.1214/aoap/998926992. |
[10] |
P. Dupuis and H. Wang, Optimal stopping with random intervention times, Adv. in Appl. Probab., 34 (2002), 141-157.
doi: 10.1239/aap/1019160954. |
[11] |
N. El Karoui, S. Peng and M. C. Quenez, Backward stochastic differential equations in finance, Mathematical Finance, 7 (1997), 1-71.
doi: 10.1111/1467-9965.00022. |
[12] |
S. Hamadène and M. Jeanblanc, On the starting and stopping problem: Application in reversible investments, Math. Oper. Res., 32 (2007), 182-192.
doi: 10.1287/moor.1060.0228. |
[13] |
S. Hamadène and J. Zhang, Switching problem and related system of reflected backward SDEs, Stochastic Processes and Their Applications, 120 (2010), 403-426.
doi: 10.1016/j.spa.2010.01.003. |
[14] |
Y. Hu and S. Tang, Multi-dimensional BSDE with oblique reflection and optimal switching, Probab. Theory Related Fields, 147 (2010), 89-121.
doi: 10.1007/s00440-009-0202-1. |
[15] |
J. Lempa, Optimal stopping with information constraint, Applied Mathematics and Optimization, 66 (2012), 147-173.
doi: 10.1007/s00245-012-9166-0. |
[16] |
G. Liang, Stochastic control representations for penalized backward stochastic differential equations, SIAM Journal on Control and Optimization, 53 (2015), 1440-1463.
doi: 10.1137/130942681. |
[17] |
G. Liang, E. Lütkebohmert and W. Wei, Funding liquidity, debt tenor structure, and creditor's belief: An exogenous dynamic debt run model, Mathematics and Financial Economics, 9 (2015), 271-302.
doi: 10.1007/s11579-015-0144-6. |
[18] |
V. Ly Vath and H. Pham, Explicit solution to an optimal switching problem in the two-regime case, SIAM Journal on Control and Optimization, 46 (2007), 395-426.
doi: 10.1137/050638783. |
[19] |
J. Ma and J. Yong, Forward-backward Stochastic Differential Equations and Their Applications, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1999. |
[20] |
É. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, 14 (1990), 55-61.
doi: 10.1016/0167-6911(90)90082-6. |
[21] |
H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Springer-Verlag, Berlin, 2009.
doi: 10.1007/978-3-540-89500-8. |
[22] |
H. Pham, V. Ly Vath and X. Y. Zhou, Optimal switching over multiple regimes, SIAM Journal on Control and Optimization, 48 (2009), 2217-2253.
doi: 10.1137/070709372. |
[23] |
A. Porchet, N. Touzi and X. Warin, Valuation of power plants by utility indifference and numerical computation, Math. Methods Oper. Res., 70 (2009), {47-75}.
doi: 10.1007/s00186-008-0231-z. |
[24] |
S. Tang and J. Yong, Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approach, Stochastics: An International Journal of Probability and Stochastic Processes, 45 (1993), 145-176.
doi: 10.1080/17442509308833860. |
[25] |
J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
doi: 10.1007/978-1-4612-1466-3. |
show all references
References:
[1] |
E. Bayraktar and M. Egami, On the one-dimensional optimal switching problem, Mathematics of Operations Research, 35 (2010), 140-159.
doi: 10.1287/moor.1090.0432. |
[2] |
E. Bayraktar and M. Ludkovski, A sequential tracking of a hidden Markov chain using point process observations, Stochastic Processes and Their Applications, 119 (2009), 1792-1822.
doi: 10.1016/j.spa.2008.09.003. |
[3] |
A. Bensoussan and J. L. Lions, Impulse Control and Quasivariational Inequalities, Gauthier-Villars, Paris, 1984. |
[4] |
K. Brekke and B. Oksendal, Optimal switching in an economic activity under uncertainty, SIAM J. Control Optim., 32 (1994), 1021-1036.
doi: 10.1137/S0363012992229835. |
[5] |
P. Briand and H. Ying, Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs, Journal of Functional Analysis, 155 (1998), 455-494.
doi: 10.1006/jfan.1997.3229. |
[6] |
R. Carmona and M. Ludkovski, Pricing asset scheduling flexibility using optimal switching, Applied Mathematical Finance, 15 (2008), 405-447.
doi: 10.1080/13504860802170507. |
[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. W. R. Darling and E. Pardoux, Backwards SDE with random terminal time and applications to semilinear elliptic PDE, The Annals of Probability, 25 (1997), 1135-1159.
doi: 10.1214/aop/1024404508. |
[9] |
K. Duckworth and M. Zervos, A model for investment decisions with switching costs, The Annals of Applied probability, 11 (2001), 239-260.
doi: 10.1214/aoap/998926992. |
[10] |
P. Dupuis and H. Wang, Optimal stopping with random intervention times, Adv. in Appl. Probab., 34 (2002), 141-157.
doi: 10.1239/aap/1019160954. |
[11] |
N. El Karoui, S. Peng and M. C. Quenez, Backward stochastic differential equations in finance, Mathematical Finance, 7 (1997), 1-71.
doi: 10.1111/1467-9965.00022. |
[12] |
S. Hamadène and M. Jeanblanc, On the starting and stopping problem: Application in reversible investments, Math. Oper. Res., 32 (2007), 182-192.
doi: 10.1287/moor.1060.0228. |
[13] |
S. Hamadène and J. Zhang, Switching problem and related system of reflected backward SDEs, Stochastic Processes and Their Applications, 120 (2010), 403-426.
doi: 10.1016/j.spa.2010.01.003. |
[14] |
Y. Hu and S. Tang, Multi-dimensional BSDE with oblique reflection and optimal switching, Probab. Theory Related Fields, 147 (2010), 89-121.
doi: 10.1007/s00440-009-0202-1. |
[15] |
J. Lempa, Optimal stopping with information constraint, Applied Mathematics and Optimization, 66 (2012), 147-173.
doi: 10.1007/s00245-012-9166-0. |
[16] |
G. Liang, Stochastic control representations for penalized backward stochastic differential equations, SIAM Journal on Control and Optimization, 53 (2015), 1440-1463.
doi: 10.1137/130942681. |
[17] |
G. Liang, E. Lütkebohmert and W. Wei, Funding liquidity, debt tenor structure, and creditor's belief: An exogenous dynamic debt run model, Mathematics and Financial Economics, 9 (2015), 271-302.
doi: 10.1007/s11579-015-0144-6. |
[18] |
V. Ly Vath and H. Pham, Explicit solution to an optimal switching problem in the two-regime case, SIAM Journal on Control and Optimization, 46 (2007), 395-426.
doi: 10.1137/050638783. |
[19] |
J. Ma and J. Yong, Forward-backward Stochastic Differential Equations and Their Applications, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1999. |
[20] |
É. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, 14 (1990), 55-61.
doi: 10.1016/0167-6911(90)90082-6. |
[21] |
H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Springer-Verlag, Berlin, 2009.
doi: 10.1007/978-3-540-89500-8. |
[22] |
H. Pham, V. Ly Vath and X. Y. Zhou, Optimal switching over multiple regimes, SIAM Journal on Control and Optimization, 48 (2009), 2217-2253.
doi: 10.1137/070709372. |
[23] |
A. Porchet, N. Touzi and X. Warin, Valuation of power plants by utility indifference and numerical computation, Math. Methods Oper. Res., 70 (2009), {47-75}.
doi: 10.1007/s00186-008-0231-z. |
[24] |
S. Tang and J. Yong, Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approach, Stochastics: An International Journal of Probability and Stochastic Processes, 45 (1993), 145-176.
doi: 10.1080/17442509308833860. |
[25] |
J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
doi: 10.1007/978-1-4612-1466-3. |
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