-
Previous Article
Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions
- NACO Home
- This Issue
-
Next Article
Maximum entropy methods for generating simulated rainfall
On Markovian solutions to Markov Chain BSDEs
1. | Mathematical Institute, University of Oxford, 24-29 St Giles, OX1 3LB, Oxford, United Kingdom, United Kingdom |
References:
[1] |
C. Bender and R. Denk, A forward scheme for backward SDEs, Stochastic Processes and their Applications, 117 (2007), 1793-1812.
doi: 10.1016/j.spa.2007.03.005. |
[2] |
B. Bouchard and N. Touzi, Discrete-time approximation and monte carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, 111 (2004), 175-206.
doi: 10.1016/j.spa.2004.01.001. |
[3] |
P. Carr, H. Geman, D. B. Madan and M. Yor, From local volatility to local Lévy models, Quantitative Finance, 4 (2004), 581-588.
doi: 10.1080/14697680400000039. |
[4] |
S. N. Cohen and R. J. Elliott, Solutions of backward stochastic differential equations on Markov chains, Communications on Stochastic Analysis, 2 (2008), 251-262. |
[5] |
S. N. Cohen and R. J. Elliott, Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions, The Annals of Applied Probability, 20 (2010), 267-311.
doi: 10.1214/09-AAP619. |
[6] |
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. |
[7] |
F. A. Longstaff and E. S. Schwartz, Valuing american options by simulation: a simple least-squares approach, Review of Financial Studies, 14 (2001), 113-147.
doi: 10.1093/rfs/14.1.113. |
[8] |
D. B. Madan, M. Pistorius and W.Schoutens, The valuation of structured products using Markov chain models, University of Maryland Working Paper, 2010. Available from http://www.ssrn.com/abstract=1563500. |
[9] |
E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, 14 (1990), 55-61.
doi: 10.1016/0167-6911(90)90082-6. |
[10] |
S. Peng., A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation, Stochastics and Stochastics Reports, 38 (1992), 119-134. |
[11] |
J. Yong and X. Y. Zhou, "Stochastic Controls, Hamiltonian Systems and HJB Equations," Springer, Berlin-Heidelberg-New York, 1999. |
show all references
References:
[1] |
C. Bender and R. Denk, A forward scheme for backward SDEs, Stochastic Processes and their Applications, 117 (2007), 1793-1812.
doi: 10.1016/j.spa.2007.03.005. |
[2] |
B. Bouchard and N. Touzi, Discrete-time approximation and monte carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, 111 (2004), 175-206.
doi: 10.1016/j.spa.2004.01.001. |
[3] |
P. Carr, H. Geman, D. B. Madan and M. Yor, From local volatility to local Lévy models, Quantitative Finance, 4 (2004), 581-588.
doi: 10.1080/14697680400000039. |
[4] |
S. N. Cohen and R. J. Elliott, Solutions of backward stochastic differential equations on Markov chains, Communications on Stochastic Analysis, 2 (2008), 251-262. |
[5] |
S. N. Cohen and R. J. Elliott, Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions, The Annals of Applied Probability, 20 (2010), 267-311.
doi: 10.1214/09-AAP619. |
[6] |
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. |
[7] |
F. A. Longstaff and E. S. Schwartz, Valuing american options by simulation: a simple least-squares approach, Review of Financial Studies, 14 (2001), 113-147.
doi: 10.1093/rfs/14.1.113. |
[8] |
D. B. Madan, M. Pistorius and W.Schoutens, The valuation of structured products using Markov chain models, University of Maryland Working Paper, 2010. Available from http://www.ssrn.com/abstract=1563500. |
[9] |
E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, 14 (1990), 55-61.
doi: 10.1016/0167-6911(90)90082-6. |
[10] |
S. Peng., A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation, Stochastics and Stochastics Reports, 38 (1992), 119-134. |
[11] |
J. Yong and X. Y. Zhou, "Stochastic Controls, Hamiltonian Systems and HJB Equations," Springer, Berlin-Heidelberg-New York, 1999. |
[1] |
Matthias Gerdts, Sven-Joachim Kimmerle. Numerical optimal control of a coupled ODE-PDE model of a truck with a fluid basin. Conference Publications, 2015, 2015 (special) : 515-524. doi: 10.3934/proc.2015.0515 |
[2] |
Jiequn Han, Jihao Long. Convergence of the deep BSDE method for coupled FBSDEs. Probability, Uncertainty and Quantitative Risk, 2020, 5 (0) : 5-. doi: 10.1186/s41546-020-00047-w |
[3] |
Alexandre Caboussat, Allison Leonard. Numerical solution and fast-slow decomposition of a population of weakly coupled systems. Conference Publications, 2009, 2009 (Special) : 123-132. doi: 10.3934/proc.2009.2009.123 |
[4] |
Ajay Jasra, Kody J. H. Law, Yaxian Xu. Markov chain simulation for multilevel Monte Carlo. Foundations of Data Science, 2021, 3 (1) : 27-47. doi: 10.3934/fods.2021004 |
[5] |
Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623 |
[6] |
Vanessa Baumgärtner, Simone Göttlich, Stephan Knapp. Feedback stabilization for a coupled PDE-ODE production system. Mathematical Control and Related Fields, 2020, 10 (2) : 405-424. doi: 10.3934/mcrf.2020003 |
[7] |
Alexandre N. Carvalho, Luciano R. N. Rocha, José A. Langa, Rafael Obaya. Structure of non-autonomous attractors for a class of diffusively coupled ODE. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022083 |
[8] |
Dmytro Marushkevych, Alexandre Popier. Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting. Probability, Uncertainty and Quantitative Risk, 2020, 5 (0) : 1-. doi: 10.1186/s41546-020-0043-5 |
[9] |
Paweł Pilarczyk. Topological-numerical approach to the existence of periodic trajectories in ODE's. Conference Publications, 2003, 2003 (Special) : 701-708. doi: 10.3934/proc.2003.2003.701 |
[10] |
Jingzhi Tie, Qing Zhang. An optimal mean-reversion trading rule under a Markov chain model. Mathematical Control and Related Fields, 2016, 6 (3) : 467-488. doi: 10.3934/mcrf.2016012 |
[11] |
Ralf Banisch, Carsten Hartmann. A sparse Markov chain approximation of LQ-type stochastic control problems. Mathematical Control and Related Fields, 2016, 6 (3) : 363-389. doi: 10.3934/mcrf.2016007 |
[12] |
Kun Fan, Yang Shen, Tak Kuen Siu, Rongming Wang. On a Markov chain approximation method for option pricing with regime switching. Journal of Industrial and Management Optimization, 2016, 12 (2) : 529-541. doi: 10.3934/jimo.2016.12.529 |
[13] |
Karl Kunisch, Sérgio S. Rodrigues. Oblique projection based stabilizing feedback for nonautonomous coupled parabolic-ode systems. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6355-6389. doi: 10.3934/dcds.2019276 |
[14] |
Maria Laura Delle Monache, Paola Goatin. A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 435-447. doi: 10.3934/dcdss.2014.7.435 |
[15] |
Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations and Control Theory, 2022, 11 (1) : 199-224. doi: 10.3934/eect.2020108 |
[16] |
Sondes khabthani, Lassaad Elasmi, François Feuillebois. Perturbation solution of the coupled Stokes-Darcy problem. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 971-990. doi: 10.3934/dcdsb.2011.15.971 |
[17] |
Tetsuya Ishiwata, Takeshi Ohtsuka. Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 893-907. doi: 10.3934/dcdss.2020390 |
[18] |
Ling Liu, Jiashan Zheng. Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3357-3377. doi: 10.3934/dcdsb.2018324 |
[19] |
Song Wang. Numerical solution of an obstacle problem with interval coefficients. Numerical Algebra, Control and Optimization, 2020, 10 (1) : 23-38. doi: 10.3934/naco.2019030 |
[20] |
Roberto Garrappa, Eleonora Messina, Antonia Vecchio. Effect of perturbation in the numerical solution of fractional differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2679-2694. doi: 10.3934/dcdsb.2017188 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]