-
Previous Article
Some linear-quadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions
- DCDS Home
- This Issue
-
Next Article
Backward stochastic Schrödinger and infinite-dimensional Hamiltonian equations
Constrained viscosity solution to the HJB equation arising in perpetual American employee stock options pricing
1. | Department of mathematics, Tongji University, Shanghai 200092 |
2. | Department of Mathematics, Tongji University, Shanghai 200092, China, China |
3. | Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom |
References:
[1] |
B. Bian, M. Dai, L. Jiang, Q. Zhang and Y. Zhong, Optimal decision for selling an illiquid stock, J. Optim. Theory Appl., 151 (2011), 402-417.
doi: 10.1007/s10957-011-9897-0. |
[2] |
J. Carpenter, The exercise and valuation of executive stock options, J. Financial Economics, 48 (1998), 127-158. |
[3] |
M. G. Crandall, H. Ishii and P. L. Lions, A user's guide to viscosity solutions, Bulletin Amer. Math. Soc., 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[4] |
W. H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975. |
[5] |
B. J. Hall and K. J. Murphy, Stock option for undiversified executives, J. Accounting Economics, 33 (2002), 3-42.
doi: 10.1016/S0165-4101(01)00050-7. |
[6] |
J. Ingersoll, The subjective and objective evaluation of incentive stock options, J. Business, 79 (2006), 453-487. |
[7] |
A. Jain and A. Subramanian, The intertemporal exercese and valuation of employee options, Accounting Review, 79 (2004), 705-743.
doi: 10.2308/accr.2004.79.3.705. |
[8] |
L. Jiang, Mathematical Modeling and Methods of Option Pricing, World Scientific Publishing Co., Inc., River Edge, NJ, 2005.
doi: 10.1142/5855. |
[9] |
R. Lambert, D. Larchker and R. Verrecchia, Portfolio considerations in valuing executive compensation, J. Accounting Research, 29 (1991), 129-149.
doi: 10.2307/2491032. |
[10] |
T. Leung and R. Sircar, Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options, Math. Finance, 19 (2009), 99-128.
doi: 10.1111/j.1467-9965.2008.00359.x. |
[11] |
L. C. G. Rogers and J. Scheinkman, Optimal exercise of executive stock options, Finance Stoch., 11 (2007), 357-372.
doi: 10.1007/s00780-007-0041-9. |
show all references
References:
[1] |
B. Bian, M. Dai, L. Jiang, Q. Zhang and Y. Zhong, Optimal decision for selling an illiquid stock, J. Optim. Theory Appl., 151 (2011), 402-417.
doi: 10.1007/s10957-011-9897-0. |
[2] |
J. Carpenter, The exercise and valuation of executive stock options, J. Financial Economics, 48 (1998), 127-158. |
[3] |
M. G. Crandall, H. Ishii and P. L. Lions, A user's guide to viscosity solutions, Bulletin Amer. Math. Soc., 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[4] |
W. H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975. |
[5] |
B. J. Hall and K. J. Murphy, Stock option for undiversified executives, J. Accounting Economics, 33 (2002), 3-42.
doi: 10.1016/S0165-4101(01)00050-7. |
[6] |
J. Ingersoll, The subjective and objective evaluation of incentive stock options, J. Business, 79 (2006), 453-487. |
[7] |
A. Jain and A. Subramanian, The intertemporal exercese and valuation of employee options, Accounting Review, 79 (2004), 705-743.
doi: 10.2308/accr.2004.79.3.705. |
[8] |
L. Jiang, Mathematical Modeling and Methods of Option Pricing, World Scientific Publishing Co., Inc., River Edge, NJ, 2005.
doi: 10.1142/5855. |
[9] |
R. Lambert, D. Larchker and R. Verrecchia, Portfolio considerations in valuing executive compensation, J. Accounting Research, 29 (1991), 129-149.
doi: 10.2307/2491032. |
[10] |
T. Leung and R. Sircar, Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options, Math. Finance, 19 (2009), 99-128.
doi: 10.1111/j.1467-9965.2008.00359.x. |
[11] |
L. C. G. Rogers and J. Scheinkman, Optimal exercise of executive stock options, Finance Stoch., 11 (2007), 357-372.
doi: 10.1007/s00780-007-0041-9. |
[1] |
Jiongmin Yong. Time-inconsistent optimal control problems and the equilibrium HJB equation. Mathematical Control and Related Fields, 2012, 2 (3) : 271-329. doi: 10.3934/mcrf.2012.2.271 |
[2] |
Ariela Briani, Hasnaa Zidani. Characterization of the value function of final state constrained control problems with BV trajectories. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1567-1587. doi: 10.3934/cpaa.2011.10.1567 |
[3] |
Ellina Grigorieva, Evgenii Khailov. Optimal control of pollution stock. Conference Publications, 2011, 2011 (Special) : 578-588. doi: 10.3934/proc.2011.2011.578 |
[4] |
Haiyang Wang, Zhen Wu. Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation. Mathematical Control and Related Fields, 2015, 5 (3) : 651-678. doi: 10.3934/mcrf.2015.5.651 |
[5] |
Nguyen Huy Chieu, Jen-Chih Yao. Subgradients of the optimal value function in a parametric discrete optimal control problem. Journal of Industrial and Management Optimization, 2010, 6 (2) : 401-410. doi: 10.3934/jimo.2010.6.401 |
[6] |
Kamil Aida-Zade, Jamila Asadova. Numerical solution to optimal control problems of oscillatory processes. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021166 |
[7] |
Zhen-Zhen Tao, Bing Sun. A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation. Electronic Research Archive, 2021, 29 (5) : 3429-3447. doi: 10.3934/era.2021046 |
[8] |
Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Fractional optimal control problems on a star graph: Optimality system and numerical solution. Mathematical Control and Related Fields, 2021, 11 (1) : 189-209. doi: 10.3934/mcrf.2020033 |
[9] |
W.C. Ip, H. Wong, Jiazhu Pan, Keke Yuan. Estimating value-at-risk for chinese stock market by switching regime ARCH model. Journal of Industrial and Management Optimization, 2006, 2 (2) : 145-163. doi: 10.3934/jimo.2006.2.145 |
[10] |
Christian Clason, Barbara Kaltenbacher. Avoiding degeneracy in the Westervelt equation by state constrained optimal control. Evolution Equations and Control Theory, 2013, 2 (2) : 281-300. doi: 10.3934/eect.2013.2.281 |
[11] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
[12] |
Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129 |
[13] |
Gökçe Dİlek Küçük, Gabil Yagub, Ercan Çelİk. On the existence and uniqueness of the solution of an optimal control problem for Schrödinger equation. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 503-512. doi: 10.3934/dcdss.2019033 |
[14] |
Radouen Ghanem, Billel Zireg. Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 275-300. doi: 10.3934/naco.2020002 |
[15] |
Steven Richardson, Song Wang. The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains. Journal of Industrial and Management Optimization, 2010, 6 (1) : 161-175. doi: 10.3934/jimo.2010.6.161 |
[16] |
Michael Grinfeld, Harbir Lamba, Rod Cross. A mesoscopic stock market model with hysteretic agents. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 403-415. doi: 10.3934/dcdsb.2013.18.403 |
[17] |
Duy Nguyen, Jingzhi Tie, Qing Zhang. Stock trading rules under a switchable market. Mathematical Control and Related Fields, 2013, 3 (2) : 209-231. doi: 10.3934/mcrf.2013.3.209 |
[18] |
Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2563-2579. doi: 10.3934/jimo.2019070 |
[19] |
Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241 |
[20] |
Eleonora Messina. Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation. Conference Publications, 2015, 2015 (special) : 826-834. doi: 10.3934/proc.2015.0826 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]