Linear-quadratic optimal control under non-Markovian switching

References

• Blair, W. P., and Sworder, D. D. 1986. Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria. International Journal of Control 21:833–841.
   Google Scholar
• Ji, Y., and Chizeck, H. J. 1990. Controllability, stabilizability, and continuous time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control 35:777–788.
   Web of Science ®Google Scholar
• Mariton, M., and Bertrand, P. 1985. Robust jump linear quadratic control: A mode stabilizing solution. IEEE Transactions on Automatic Control AC-30:1145–1147.
   Web of Science ®Google Scholar
• Mao, X. 1999. Stability of stochastic differential with Markovian switching. Stochastic Process Applications 79:45–67.
   Web of Science ®Google Scholar
• Di Masi, G. B., Kabanov, Y. M., and Runggaldier, W. J. 1994. Mean variance hedging of options on stocks with Markov volatility. Theory of Probability and Applications 39:173–181.
   Web of Science ®Google Scholar
• Moller, C. M. 1995. Stochastic differential equations for ruin probability. Journal of Applied Probability 32:74–89.
   Web of Science ®Google Scholar
• Rolski, T., Schmidli, H., Schmidt, V., and Teugels, J. 1999. Stochastic Processes for Insurance and Finance. New York: Wiley.
   Google Scholar
• Yang, H., and Yin, H. 2004. Ruin probability for a model under Markovian switching regime. In: Lai, T. L., Yang, H., Yung, S. P., eds., Probability, Finance and Insurance. New York: World Science, pp. 206–217.
   Google Scholar
• Zhang, Q. 2001. Stock trading: An optimal selling rule. SIAM Journal on Control and Optimization 40:64–87.
   Web of Science ®Google Scholar
• Kushner, H. J. 1990. Numerical methods for stochastic control problems in continuous time. SIAM Journal on Control and Optimization 28:999–1048.
   Web of Science ®Google Scholar
• Costa, O. L. V., Fragoso, M. D., and Todorov, M. G. 2013. Continuous-Time Markov Jump Linear Systems (Probability and its Applications) (New York). Heidelberg: Springer.
   Google Scholar
• Dragan, V., Morozan, T., and Stoica, A. 2013. Mathematical Methods in Robust Control of Linear Stochastic Systems. 2nd ed. New York: Springer.
   Google Scholar
• Bismut, J.-M. 1976. Linear quadratic optimal stochastic control with random coefficients. SIAM Journal on Control and Optimization 14:419–444.
   Web of Science ®Google Scholar
• Peng, S. 1992. Stochastic Hamilton-Jacobi-Bellman equations. SIAM Journal on Control and Optimization 30(2):284–304.
   Web of Science ®Google Scholar
• Kohlmann, M., and Tang, S. 2001. New developments in backward stochastic Riccati equations and their applications. In: Kohlmann, M., Tang, S., eds. Mathematical Finance (Konstanz, 2000), Trends in Mathematics. Basel: Birkhäuser, pp. 194–214.
   Google Scholar
• Kohlmann, M., and Tang, S. 2002. Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging. Stochastic Processes and their Applications 97:1255–288.
   Web of Science ®Google Scholar
• Kohlmann, M., and Tang, S. 2003. Multidimensional backward stochastic Riccati equations and applications. SIAM Journal on Control and Optimization 41:1696–1721.
   Web of Science ®Google Scholar
• Tang, S. 2003. General linear quadratic optimal stochastic control problems with random coefficients: Linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM Journal on Control and Optimization 42(1):53–75.
   Web of Science ®Google Scholar
• Guatteri, G., and Masiero, F. 2009. Infinite horizon and ergodic optimal quadratic control for an affine equation with stochastic coefficients. SIAM Journal on Control and Optimization 48(3):1600–1631.
   Web of Science ®Google Scholar
• Guatteri, G., and Masiero, F. 2009. Ergodic optimal quadratic control for an affine equation with stochastic and stationary coefficients. Systems & Control Letters 58(3):169–177.
   Web of Science ®Google Scholar
• Hu, Y., and Oksendal, B. 2008. Partial information linear quadratic control for jump diffusion. SIAM Journal on Control and Optimization 47:1744–1761.
   Web of Science ®Google Scholar
• Meng, Q. 2014. General linear quadratic optimal stochastic control problem driven by a Brownian motion and a Poisson random martingale measure with random coefficients. Stochastic Analysis and Applications 32:88–109.
   Web of Science ®Google Scholar
• Shi, J., and Wu, Z. 2015. Backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure. Stochastics 87(1):1–29.
   Google Scholar
• Bandini, E. 2015. Existence and uniqueness for BSDEs driven by a general random measure, possibly non quasi-left-continuous. Electronic Communications in Probability 20(71):1–13.
   Google Scholar
• Becherer, D. 2006. Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging. Annals of Applied Probability 16(4):2027–2054.
   Web of Science ®Google Scholar
• Confortola, F., and Fuhrman, M. 2013. Backward stochastic differential equations and optimal control of marked point processes. SIAM Journal on Control and Optimization 51(5):3592–3623.
   Web of Science ®Google Scholar
• Confortola, F., Fuhrman, M., and Jacod, J. 2016. Backward stochastic differential equations driven by a marked point process: An elementary approach, with an application to optimal control. Annals of Applied Probability 26(3):1743–1773.
   Web of Science ®Google Scholar
• Jacod, J. 1974/75. Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 31:235–253.
   Google Scholar
• Brémaud, P. 1981. Point Processes and Queues, Martingale Dynamics (Springer Series in Statistics). New York: Springer.
   Google Scholar
• Brandt, A., and Last, G. 1995. Marked Point Processes on the Real Line. The Dynamic Approach. New York: Springer.
   Google Scholar
• Gihman, I. I., and Skorohod, A. V. 1972. Stochastic Differential Equations. Ergebnisse der Mathematik und Ihrer Grenzgebiete, Band 72. New York-Heidelberg: Springer-Verlag.
   Google Scholar
• Ikeda, N., and Watanabe, S. 1981. Stochastic Differential Equations and Diffusion Processes (North-Holland Mathematical Library). Vol. 24. Amsterdam-New York; Tokyo: North-Holland Publishing Co.; Kodansha, Ltd., pp. xiv+464.
   Google Scholar
• Protter, P. 1990. Stochastic Integration and Differential Equations. A New Approach (Applications of Mathematics (New York)). Vol. 21. Berlin: Springer-Verlag.
   Google Scholar
• Tang S., Li X., 1994. Necessary conditions for optimal control of systems with random jumps. SIAM Journal on Control and Optimization 32:1447–1475.
   Web of Science ®Google Scholar
• Barles, G., Buckdahn, R., and Pardoux, E. 1997. Backward stochastic differential equations and integral-partial differential equations. Stochastics and Stochastics Reports 60:57–83.
   Google Scholar
• Pardoux, E. 1997. Generalized discontinuous backward stochastic differential equations. In: Backward Stochastic Differential Equations, (Pitman Res. Notes Math. Ser. Vol. 364), Harlow: Longman, pp. 207–219.
   Google Scholar
• He, S. W., Wang, J. G., and Yan, J. A. 1992. Semimartingale Theory and Stochastic Calculus. Kexue Chubanshe (Science Press), Beijing; Boca Raton, FL: CRC Press.
   Google Scholar
• Bensoussan, A., Da Prato, G., Delfour, M. C., and Mitter, S. K. 1992. Representation and Control of Infinite Dimensional Systems: Vol. 1 (Systems & Control: Foundations & Applications). Boston, MA: Birkhäuser Boston, Inc.
   Google Scholar
• Tessitore, G. 1992. Some remarks on the Riccati equation arising in an optimal control problem with state- and control-dependent noise. SIAM Journal on Control and Optimization, 30:717–744.
   Web of Science ®Google Scholar