Paper:

# Optimistic Value Model of Uncertain Linear Quadratic Optimal Control with Jump

## Liubao Deng^{*} and Yuefen Chen^{**}

^{*}School of Finance, Anhui University of Finance and Economics

962 Caoshan Road, Bengbu 233030, China

^{*} College of Mathematics and Information Science, Xinyang Normal University

237 Nanhu Road, Xinyang 464000, China

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.20 No.2, pp. 189-196, 2016.

- [1] R. Kalman, “Contribution to the theory of optimal control,” Boletin Sociedad Matematica Mexicana, Vol.5, No.1, pp. 102-119, 1960.
- [2] W. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM J. on Control and Optimization, Vol.6, No.1, pp. 681-697, 1968.
- [3] W. Wonham, “Random differential equation in control theory,” Probabilistic Method in Applied Mathematics, A. T. Bharucha-Reid, Ed. Chapt.2., Academic Press, New York. 1970.
- [4] J. Bismut, “Linear quadratic optimal stochastic control with random coefficients,” SIAM J. on Control an Optimization, Vol.14, No.3, pp. 419-444, 1976.
- [5] A. Bonsoussan, “A Stochastic Control of Partially Observed Systems,” Cambridge Univ. Press, Cambridge, UK, 1992.
- [6] M. Davis, “Linear Estimation and Stochastic Control,” Chapman and Hall, London, UK, 1977.
- [7] S. Chen, X. Li, and X. Zhou, “Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs,” SIAM J. on Control and Optimization, Vol.36, No.5, pp. 1685-1702, 1998.
- [8] H. Wu and X. Zhou, “Characterizing all optimal controls for an indefinite stochastic linear quadratic control problem,” IEEE Trans. on Automatic Control, Vol.47, No.7, pp. 1119-1122, 2002.
- [9] X. Zhou and D. Li, “Continuous-time mean-variance portfolio selection: A stochastic LQ framework,” Applied Mathematics and Optimization, Vol.42, No.1, pp. 19-33, 2009.
- [10] B. Liu, “Why is there a need for uncertainty theory?,” J. of Uncertain Systems, Vol.6, No.1, pp. 3-10, 2012.
- [11] B. Liu, “Uncertainty Theory (2
^{nd}Ed.),” Springer-Verlag, Berlin, 2007. - [12] Y. Zhu, “Uncertain optimal control with application to a portfolio selection model,” Cybernetics and Systems, Vol.41, No.7, pp. 535-547, 2010.
- [13] Y. Kang and Y. Zhu, “Bang-bang optimal control for multi-stage uncertain systems,” Information: An Int. Interdisciplinary J., Vol.15, No.8, pp. 3229-3238, 2012.
- [14] X. Xu and Y. Zhu, “Uncertain bang-bang control for continuous time model,” Cybernetics and Systems: An Int. J., Vol.43, No.6, pp. 515-527, 2012.
- [15] H. Yan and Y. Zhu, “Bang-bang control model for uncertain switched systems,” Applied Mathematical Modelling, in press, Online available: http://dx.doi.org/10.1016/j.apm.2014.10.042, 2014.
- [16] R. Chen and Y. Zhu, “An optimal control model for uncertain systems with time-delay,” J. of the Operations Research Society of Japan, Vol.56, No.4, pp. 243-256, 2013.
- [17] K. Yao and Z. Qin, “An uncertain control model with application to production inventory system,” Proc. 12th Asia Pacific Industrial Engineering and Management Systems Conf., Beijing, China, pp. 972-977, 2011.
- [18] L. Deng and Y. Zhu, “Uncertain optimal control with jump,” ICIC Express Letters, Part B: Applications, Vol.3, No.2, pp. 419-424, 2012.
- [19] L. Deng and Y. Zhu, “An uncertain optimal control model with
*n*jumps and application,” Computer Science and Information Systems, Vol.9, No.4, pp. 1453-1468, 2012. - [20] L. Deng and Y. Zhu, “Uncertain optimal control of linear quadratic models with jump,” Mathematical and Computer Modelling, Vol.57, No.9-10, pp. 2432-2441, 2013.
- [21] L. Deng, “Multidimensional uncertain optimal control of linear quadratic models with jump,” J. of Computational Information Systems, Vol.8, No.18, pp. 7441-7448, 2012.
- [22] L. Sheng and Y. Zhu, “Optimistic value model of uncertain optimal control,” Int. J. of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.21, No.Suppl.1, pp. 75-83, 2013.
- [23] L. Deng, “Optimistic value model of uncertain optimal control with jump and application in finance,” http://orsc.edu.cn/online/150118.pdf., 2014.
- [24] F. Harris, “How many parts to make at once, Factory,” The Magazine of Management, No.10, pp. 135-136, 152, 1913; reprinted in Operations Research, Vol.38, pp. 947-950, 1990.
- [25] H. Simon, “Dynamic Programming under Uncertainty with a Quadratic Criterion Function,” Econometrica, Vol.24, pp. 74-81, 1956.
- [26] C. Holt, F. Modigliani, J. Muth, and H. Simon, “Planning Production, Inventories, and Work Force,” Prentice-Hall, Englewood Cliffs, New Jersey, 1960.
- [27] C. Huang, L. Fan, and L. Erickson, “Optimum Production Planning by the Maximum Principle,” Management Science, No.13, pp. 751-755, 1967.
- [28] R. Merton, “Optimal consumption and portfolio rules in a continuous time model,” J. of Economic Theory, No.3, pp. 373-413, 1971.
- [29] S. Sethi and G. Thompson, “Optimal Control Theory: Application to Management Science,” Martinus Nijhoff Publishing, 1981.
- [30] Y. Zheng, “Optimal Control Policy for Stochastic Inventory Systems with Markovian Discount Opportunities,” Operations Research, Vol.42, No.4, pp. 721-738, 1994.
- [31] X. Ouyang, “Stochastic Optimization of Inventory Control,” Mathematica Applicata, Vol.23, No.2, pp. 445-449, 2010.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.