-
Previous Article
Upper risk bounds in internal factor models with constrained specification sets
- PUQR Home
- This Issue
-
Next Article
Convergence of the deep BSDE method for coupled FBSDEs
Uncertainty and filtering of hidden Markov models in discrete time
Mathematical Institute, University of Oxford, Woodstock Road, Oxford, UK |
References:
[1] |
Allan, A.L. and S.N. Cohen. (2019a). Parameter uncertainty in the Kalman–Bucy filter, SIAM J. Control Optim. 57, no. 3, 1646–1671., |
[2] |
Allan, A.L. and S.N. Cohen. (2020). Pathwise Stochastic Control with Applications to Robust Filtering, Ann. Appl. Prob. arXiv::1902.05434., |
[3] |
Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath. (1999). Coherent measures of risk, Math. Finan. 9, no. 3, 203–228., |
[4] |
Başar, T. and P. Bernhard. (1991). H∞-Optimal Control and Related Minimax Design Problems, A Dynamic Game Approach, Birkhäuser, Basel., |
[5] |
Bain, A. and D. Crisan. (2009). Fundamentals of Stochastic Filtering, Springer, Berlin–Heidelberg–New York., |
[6] |
Bielecki, T.R., T. Chen, and I. Cialenco. (2017). Recursive construction of confidence regions, Electron. J. Stat. 11, no. 2, 4674–4700., |
[7] |
Boel, R.K., M.R. James, and I.R. Petersen. (2002). Robustness and risk-sensitive filtering, IEEE Trans. Autom. Control 47, no. 3, 451–461., |
[8] |
Cohen, S.N. and R.J. Elliott. (2010). A general theory of finite state backward stochastic difference equations, Stoch. Process. Appl. 120, no. 4, 442–466., |
[9] |
Cohen, S.N. and R.J. Elliott. (2011). Backward stochastic difference equations and nearly-time-consistent nonlinear expectations, SIAM J. Control Optim. 49, no. 1, 125–139., |
[10] |
Cohen, S.N. and R.J. Elliott. (2015). Stochastic Calculus and Applications, 2nd ed., Birkhäuser, New York., |
[11] |
Cohen, S.N. (2017). Data-driven nonlinear expectations for statistical uncertainty in decisions, Electron. J. Stat. 11, no. 1, 1858–1889., |
[12] |
Delbaen, F., S. Peng, and E. Rosazza Gianin. (2010). Representation of the penalty term of dynamic concave utilities, Finan. Stochast. 14, no. 3, 449–472., |
[13] |
Dey, S. and J.B. Moore. (1995). Risk-sensitive filtering and smoothing for hidden Markov models, Syst. Control Lett. 25, 361–366., |
[14] |
Douc, R., E. Moulines, J. Olsson, and R. van Handel. (2011). Consistency of the maximum likelihood estimator for general hidden Markov models, Ann. Stat. 39, no. 1, 474–513., |
[15] |
Duffie, D. and L.G. Epstein. (1992). Asset pricing with stochastic differential utility, Rev. Finan. Stud. 5, no. 3, 411–436., |
[16] |
El Karoui, N., S. Peng, and M.C. Quenez. (1997). Backward stochastic differential equations in finance, Math. Finan. 7, no. 1, 1–71., |
[17] |
Epstein, L.G. and M. Schneider. (2003). Recursive multiple-priors, J. Econ. Theory 113, 1–31., |
[18] |
Fagin, R. and J. Halpern. (1990). A new approach to updating beliefs, AUAI Press, Corvallis., |
[19] |
Föllmer, H. and A. Schied. (2002a). Convex measures of risk and trading constraints, Finan. Stochast. 6, 429–447., |
[20] |
Föllmer, H. and A. Schied. (2002b). Stochastic Finance: An Introduction in Discrete Time. Studies in Mathematics 27, de Gruyter, Berlin-New York., |
[21] |
Frittelli, M. and E. Rosazza Gianin. (2002). Putting order in risk measures, J. Bank. Financ. 26, no. 7, 1473–1486., |
[22] |
Graf, S. (1980). A Radon–Nikodym theorem for capacities, J. für die reine und angewandte Mathematik 320, 192–214., |
[23] |
Grimble, M.J. and A. El Sayed. (1990). Solution of the H∞ optimal linear filtering problem for discretetime systems, Trans. Acoust. Speech Sig. Process. IEEE 38, no. 7., |
[24] |
Hansen, L.P. and T.J. Sargent. (2005). Robust estimation and control under commitment, J. Econ. Theory 124, 258–301., |
[25] |
Hansen, L.P. and T.J. Sargent. (2007). Recursive robust estimation and control without commitment, J. Econ. Theory 136, no. 1, 1–27., |
[26] |
Hansen, L.P. and T.J. Sargent. (2008). Robustness, Princeton University Press, Princeton., |
[27] |
Huber, P.J. and E.M. Roncetti. (2009). Robust Statistics, 2nd edn., Wiley, Hoboken., |
[28] |
James, M.R., J.S. Baras, and R.J. Elliott. (1994). Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems, Trans. Autom. Control IEEE 39, no. 4, 780–792. https://doi.org/10.1109/9.286253., |
[29] |
Kalman, R.E. (1960). A new approach to linear filtering and prediction problems, J. Basic Eng. ASME 82, 33–45., |
[30] |
Kalman, R.E. and R.S. Bucy. (1961). New results in linear filtering and prediction theory, J. Basic Eng. ASME 83, 95–108., |
[31] |
Keynes, J.M. (1921). A Treatise on Probability, Macmillan and Co., New York. Reprint BN Publishing, 2008., |
[32] |
Knight, F.H. (1921). Risk, Uncertainty and Profit, Houghton Mifflin, Boston. reprint Dover 2006., |
[33] |
Kupper, M. and W. Schachermayer. (2009). Representation results for law invariant time consistent functions, Math. Financ. Econ. 2, no. 3, 189–210., |
[34] |
Leroux, B.G. (1992). Maximum-likelihood estimation for hidden Markov models, Stoch. Process. Appl. 40, 127–143., |
[35] |
Peng, S. (2010). Nonlinear Expectations and Stochastic Calculus under Uncertainty, arxiv::1002.4546v1., |
[36] |
Riedel, F. (2004). Dynamic coherent risk measures, Stochast. Process. Appl. 112, no. 2, 185–200., |
[37] |
Rockafellar, R.T., S. Uryasev, and M. Zabarankin. (2006). Generalized deviations in risk analysis, Finan. Stochast. 10, 51–74., |
[38] |
Wald, A. (1945). Statistical decision functions which minimize the maximum risk, Ann. Math. 46, no. 2, 265–280., |
[39] |
Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London., |
[40] |
Wonham, W.N. (1965). Some applications of stochastic differential equations to optimal nonlinear filtering, SIAM J. Control 2, 347–369., |
[41] |
Zhang, J., Y. Xia, and P. Shi. (2009). Parameter-dependent robust H∞ filtering for uncertain discrete-time systems, Automatica 45, 560–565., |
show all references
References:
[1] |
Allan, A.L. and S.N. Cohen. (2019a). Parameter uncertainty in the Kalman–Bucy filter, SIAM J. Control Optim. 57, no. 3, 1646–1671., |
[2] |
Allan, A.L. and S.N. Cohen. (2020). Pathwise Stochastic Control with Applications to Robust Filtering, Ann. Appl. Prob. arXiv::1902.05434., |
[3] |
Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath. (1999). Coherent measures of risk, Math. Finan. 9, no. 3, 203–228., |
[4] |
Başar, T. and P. Bernhard. (1991). H∞-Optimal Control and Related Minimax Design Problems, A Dynamic Game Approach, Birkhäuser, Basel., |
[5] |
Bain, A. and D. Crisan. (2009). Fundamentals of Stochastic Filtering, Springer, Berlin–Heidelberg–New York., |
[6] |
Bielecki, T.R., T. Chen, and I. Cialenco. (2017). Recursive construction of confidence regions, Electron. J. Stat. 11, no. 2, 4674–4700., |
[7] |
Boel, R.K., M.R. James, and I.R. Petersen. (2002). Robustness and risk-sensitive filtering, IEEE Trans. Autom. Control 47, no. 3, 451–461., |
[8] |
Cohen, S.N. and R.J. Elliott. (2010). A general theory of finite state backward stochastic difference equations, Stoch. Process. Appl. 120, no. 4, 442–466., |
[9] |
Cohen, S.N. and R.J. Elliott. (2011). Backward stochastic difference equations and nearly-time-consistent nonlinear expectations, SIAM J. Control Optim. 49, no. 1, 125–139., |
[10] |
Cohen, S.N. and R.J. Elliott. (2015). Stochastic Calculus and Applications, 2nd ed., Birkhäuser, New York., |
[11] |
Cohen, S.N. (2017). Data-driven nonlinear expectations for statistical uncertainty in decisions, Electron. J. Stat. 11, no. 1, 1858–1889., |
[12] |
Delbaen, F., S. Peng, and E. Rosazza Gianin. (2010). Representation of the penalty term of dynamic concave utilities, Finan. Stochast. 14, no. 3, 449–472., |
[13] |
Dey, S. and J.B. Moore. (1995). Risk-sensitive filtering and smoothing for hidden Markov models, Syst. Control Lett. 25, 361–366., |
[14] |
Douc, R., E. Moulines, J. Olsson, and R. van Handel. (2011). Consistency of the maximum likelihood estimator for general hidden Markov models, Ann. Stat. 39, no. 1, 474–513., |
[15] |
Duffie, D. and L.G. Epstein. (1992). Asset pricing with stochastic differential utility, Rev. Finan. Stud. 5, no. 3, 411–436., |
[16] |
El Karoui, N., S. Peng, and M.C. Quenez. (1997). Backward stochastic differential equations in finance, Math. Finan. 7, no. 1, 1–71., |
[17] |
Epstein, L.G. and M. Schneider. (2003). Recursive multiple-priors, J. Econ. Theory 113, 1–31., |
[18] |
Fagin, R. and J. Halpern. (1990). A new approach to updating beliefs, AUAI Press, Corvallis., |
[19] |
Föllmer, H. and A. Schied. (2002a). Convex measures of risk and trading constraints, Finan. Stochast. 6, 429–447., |
[20] |
Föllmer, H. and A. Schied. (2002b). Stochastic Finance: An Introduction in Discrete Time. Studies in Mathematics 27, de Gruyter, Berlin-New York., |
[21] |
Frittelli, M. and E. Rosazza Gianin. (2002). Putting order in risk measures, J. Bank. Financ. 26, no. 7, 1473–1486., |
[22] |
Graf, S. (1980). A Radon–Nikodym theorem for capacities, J. für die reine und angewandte Mathematik 320, 192–214., |
[23] |
Grimble, M.J. and A. El Sayed. (1990). Solution of the H∞ optimal linear filtering problem for discretetime systems, Trans. Acoust. Speech Sig. Process. IEEE 38, no. 7., |
[24] |
Hansen, L.P. and T.J. Sargent. (2005). Robust estimation and control under commitment, J. Econ. Theory 124, 258–301., |
[25] |
Hansen, L.P. and T.J. Sargent. (2007). Recursive robust estimation and control without commitment, J. Econ. Theory 136, no. 1, 1–27., |
[26] |
Hansen, L.P. and T.J. Sargent. (2008). Robustness, Princeton University Press, Princeton., |
[27] |
Huber, P.J. and E.M. Roncetti. (2009). Robust Statistics, 2nd edn., Wiley, Hoboken., |
[28] |
James, M.R., J.S. Baras, and R.J. Elliott. (1994). Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems, Trans. Autom. Control IEEE 39, no. 4, 780–792. https://doi.org/10.1109/9.286253., |
[29] |
Kalman, R.E. (1960). A new approach to linear filtering and prediction problems, J. Basic Eng. ASME 82, 33–45., |
[30] |
Kalman, R.E. and R.S. Bucy. (1961). New results in linear filtering and prediction theory, J. Basic Eng. ASME 83, 95–108., |
[31] |
Keynes, J.M. (1921). A Treatise on Probability, Macmillan and Co., New York. Reprint BN Publishing, 2008., |
[32] |
Knight, F.H. (1921). Risk, Uncertainty and Profit, Houghton Mifflin, Boston. reprint Dover 2006., |
[33] |
Kupper, M. and W. Schachermayer. (2009). Representation results for law invariant time consistent functions, Math. Financ. Econ. 2, no. 3, 189–210., |
[34] |
Leroux, B.G. (1992). Maximum-likelihood estimation for hidden Markov models, Stoch. Process. Appl. 40, 127–143., |
[35] |
Peng, S. (2010). Nonlinear Expectations and Stochastic Calculus under Uncertainty, arxiv::1002.4546v1., |
[36] |
Riedel, F. (2004). Dynamic coherent risk measures, Stochast. Process. Appl. 112, no. 2, 185–200., |
[37] |
Rockafellar, R.T., S. Uryasev, and M. Zabarankin. (2006). Generalized deviations in risk analysis, Finan. Stochast. 10, 51–74., |
[38] |
Wald, A. (1945). Statistical decision functions which minimize the maximum risk, Ann. Math. 46, no. 2, 265–280., |
[39] |
Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London., |
[40] |
Wonham, W.N. (1965). Some applications of stochastic differential equations to optimal nonlinear filtering, SIAM J. Control 2, 347–369., |
[41] |
Zhang, J., Y. Xia, and P. Shi. (2009). Parameter-dependent robust H∞ filtering for uncertain discrete-time systems, Automatica 45, 560–565., |
[1] |
Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019 |
[2] |
Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077 |
[3] |
Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020046 |
[4] |
Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020107 |
[5] |
Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Fractional optimal control problems on a star graph: Optimality system and numerical solution. Mathematical Control & Related Fields, 2021, 11 (1) : 189-209. doi: 10.3934/mcrf.2020033 |
[6] |
Christian Clason, Vu Huu Nhu, Arnd Rösch. Optimal control of a non-smooth quasilinear elliptic equation. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020052 |
[7] |
Hongbo Guan, Yong Yang, Huiqing Zhu. A nonuniform anisotropic FEM for elliptic boundary layer optimal control problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1711-1722. doi: 10.3934/dcdsb.2020179 |
[8] |
A. Alessandri, F. Bedouhene, D. Bouhadjra, A. Zemouche, P. Bagnerini. Observer-based control for a class of hybrid linear and nonlinear systems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1213-1231. doi: 10.3934/dcdss.2020376 |
[9] |
Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020347 |
[10] |
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Deep quench approximation and optimal control of general Cahn–Hilliard systems with fractional operators and double obstacle potentials. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 243-271. doi: 10.3934/dcdss.2020213 |
[11] |
Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020110 |
[12] |
Elimhan N. Mahmudov. Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions. Evolution Equations & Control Theory, 2021, 10 (1) : 37-59. doi: 10.3934/eect.2020051 |
[13] |
Lars Grüne, Roberto Guglielmi. On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Mathematical Control & Related Fields, 2021, 11 (1) : 169-188. doi: 10.3934/mcrf.2020032 |
[14] |
Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026 |
[15] |
Arthur Fleig, Lars Grüne. Strict dissipativity analysis for classes of optimal control problems involving probability density functions. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020053 |
[16] |
Yuan Xu, Xin Jin, Saiwei Wang, Yang Tang. Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1495-1518. doi: 10.3934/dcdss.2020377 |
[17] |
Héctor Barge. Čech cohomology, homoclinic trajectories and robustness of non-saddle sets. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020381 |
[18] |
Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020 doi: 10.3934/jgm.2020032 |
[19] |
Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65 |
[20] |
Kalikinkar Mandal, Guang Gong. On ideal $ t $-tuple distribution of orthogonal functions in filtering de bruijn generators. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020125 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]