Uncertainty and filtering of hidden Markov models in discrete time

Samuel N. Cohen1
1Mathematical Institute, University of Oxford, Oxford, UK

Tóm tắt

Từ khóa


Tài liệu tham khảo

Allan, A. L., Cohen, S. N.: Parameter uncertainty in the Kalman–Bucy filter. SIAM J. Control Optim. 57(3), 1646–1671 (2019a).

Allan, A. L., Cohen, S. N.: Pathwise Stochastic Control with Applications to Robust Filtering. Ann. Appl. Prob. (2020). arXiv::1902.05434.

Artzner, P., Delbaen, F., Eber, J. -M., Heath, D.: Coherent measures of risk. Math. Finan. 9(3), 203–228 (1999).

Başar, T., Bernhard, P.: H∞-Optimal Control and Related Minimax Design Problems, A Dynamic Game Approach. Birkhäuser, Basel (1991).

Bain, A., Crisan, D.: Fundamentals of Stochastic Filtering. Springer, Berlin–Heidelberg–New York (2009).

Bielecki, T. R., Chen, T., Cialenco, I.: Recursive construction of confidence regions. Electron. J. Stat. 11(2), 4674–4700 (2017).

Boel, R. K., James, M. R., Petersen, I. R.: Robustness and risk-sensitive filtering. IEEE Trans. Autom. Control. 47(3), 451–461 (2002).

Cohen, S. N., Elliott, R. J.: A general theory of finite state backward stochastic difference equations. Stoch. Process. Appl. 120(4), 442–466 (2010).

Cohen, S. N., Elliott, R. J.: Backward stochastic difference equations and nearly-time-consistent nonlinear expectations. SIAM J. Control Optim. 49(1), 125–139 (2011).

Cohen, S. N., Elliott, R. J.: Stochastic Calculus and Applications. 2nd ed. Birkhäuser, New York (2015).

Cohen, S. N.: Data-driven nonlinear expectations for statistical uncertainty in decisions. Electron. J. Stat. 11(1), 1858–1889 (2017).

Delbaen, F., Peng, S., Rosazza Gianin, E.: Representation of the penalty term of dynamic concave utilities. Finan. Stochast. 14(3), 449–472 (2010).

Dey, S., Moore, J. B.: Risk-sensitive filtering and smoothing for hidden Markov models. Syst. Control Lett. 25, 361–366 (1995).

Douc, R., Moulines, E., Olsson, J., van Handel, R.: Consistency of the maximum likelihood estimator for general hidden Markov models. Ann. Stat. 39(1), 474–513 (2011).

Duffie, D., Epstein, L. G.: Asset pricing with stochastic differential utility. Rev. Finan. Stud. 5(3), 411–436 (1992).

El Karoui, N., Peng, S., Quenez, M. C.: Backward stochastic differential equations in finance. Math. Finan. 7(1), 1–71 (1997).

Epstein, L. G., Schneider, M.: Recursive multiple-priors. J. Econ. Theory. 113, 1–31 (2003).

Fagin, R., Halpern, J.: A new approach to updating beliefs. In: Proceedings of the Sixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-90), pp. 317–325. AUAI Press, Corvallis (1990).

Föllmer, H., Schied, A.: Convex measures of risk and trading constraints. Finan. Stochast. 6, 429–447 (2002a).

Föllmer, H., Schied, A.: Stochastic Finance: An Introduction in Discrete Time. Studies in Mathematics 27. de Gruyter, Berlin-New York (2002b).

Frittelli, M., Rosazza Gianin, E.: Putting order in risk measures. J. Bank. Financ. 26(7), 1473–1486 (2002).

Graf, S.: A Radon–Nikodym theorem for capacities. J. für die reine und angewandte Mathematik. 320, 192–214 (1980).

Grimble, M. J., El Sayed, A.: Solution of the H∞ optimal linear filtering problem for discrete-time systems. Trans. Acoust. Speech Sig. Process. IEEE. 38(7) (1990).

Hansen, L. P., Sargent, T. J.: Robust estimation and control under commitment. J. Econ. Theory. 124, 258–301 (2005).

Hansen, L. P., Sargent, T. J.: Recursive robust estimation and control without commitment. J. Econ. Theory. 136(1), 1–27 (2007).

Hansen, L. P., Sargent, T. J.: Robustness. Princeton University Press, Princeton (2008).

Huber, P. J., Roncetti, E. M.: Robust Statistics, 2nd edn.Wiley, Hoboken (2009).

James, M. R., Baras, J. S., Elliott, R. J.: Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems. Trans. Autom. Control IEEE. 39(4), 780–792 (1994). https://doi.org/10.1109/9.286253 .

Kalman, R. E.: A new approach to linear filtering and prediction problems. J. Basic Eng. ASME. 82, 33–45 (1960).

Kalman, R. E., Bucy, R. S.: New results in linear filtering and prediction theory. J. Basic Eng. ASME. 83, 95–108 (1961).

Keynes, J. M.: A Treatise on Probability. Macmillan and Co., New York (1921). Reprint BN Publishing, 2008.

Knight, F. H.: Risk, Uncertainty and Profit. Houghton Mifflin, Boston (1921). reprint Dover 2006.

Kupper, M., Schachermayer, W.: Representation results for law invariant time consistent functions. Math. Financ. Econ. 2(3), 189–210 (2009).

Leroux, B. G.: Maximum-likelihood estimation for hidden Markov models. Stoch. Process. Appl. 40, 127–143 (1992).

Peng, S.: Nonlinear Expectations and Stochastic Calculus under Uncertainty. arxiv::1002.4546v1 (2010).

Riedel, F.: Dynamic coherent risk measures. Stochast. Process. Appl. 112(2), 185–200 (2004).

Rockafellar, R. T., Uryasev, S., Zabarankin, M.: Generalized deviations in risk analysis. Finan. Stochast. 10, 51–74 (2006).

Wald, A.: Statistical decision functions which minimize the maximum risk. Ann. Math. 46(2), 265–280 (1945).

Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991).

Wonham, W. N.: Some applications of stochastic differential equations to optimal nonlinear filtering. SIAM J. Control. 2, 347–369 (1965).

Zhang, J., Xia, Y., Shi, P.: Parameter-dependent robust H∞ filtering for uncertain discrete-time systems. Automatica. 45, 560–565 (2009).