H∞-Optimal Control for Robust Financial Asset and Input Purchasing Decisions

ABSTRACT

This analysis formulates an approach for converting minimax LQ (linear-quadratic) tracking problems into LQ regulator designs, and develops a Matlab application program to calculate an H-infinity robust control for discrete-time systems with perfect state measurements. It uses simulations to explore examples in financial asset decisions and utility input purchasing, in order to demonstrate the method. The user is allowed to choose the parameters, and the program computes the generalized Riccati Equation conditions for the existence of a saddle-point solution. Given that it exists, the program computes a minimax solution to the linear quadratic (LQ) soft-constrained game with constant coefficients for a general scalar model, and also to a class of matrix systems. The user can set the bound to achieve disturbance attenuation.

Cite this paper

D. Hudgins and J. Na, "H∞-Optimal Control for Robust Financial Asset and Input Purchasing Decisions,"*Journal of Mathematical Finance*, Vol. 3 No. 3, 2013, pp. 335-346. doi: 10.4236/jmf.2013.33034.

D. Hudgins and J. Na, "H∞-Optimal Control for Robust Financial Asset and Input Purchasing Decisions,"

References

[1] T. Basar and P. Bernhard, “H∞-Optimal Control and Related Minimax Design Problems,” Birkhauser, Boston, 1991.

[2] G. Chow, “Analysis and Control of Dynamic Economic Systems,” John Wiley and Sons, New York, 1975.

[3] A. Sage and C. White, “Optimum Systems Control,” 2nd Edition, E Prentice Hall, Engelwood Cliffs, 1977.

[4] D. Kendrick, “Stochastic Control for Econometric Models,” McGraw Hill, New York, 1981.

[5] A. Tornell, “Robust-H-Infinity Forecasting and Asset Pricing Anomalies,” NBER Working Paper No. 7753, 2000.

[6] T. Basar, “On the Application of Differential Game Theory in Robust Controller Design for Economic Systems,” In: G. Feichtinger, Ed., Dynamic Economic Models and Optimal Control, North-Holland, Amsterdam, 1992, pp. 269-278.

[7] L. Hansen, T. Sargent and T. Tallarini, “Robust Permanent Income and Pricing,” Review of Economic Studies, Vol. 66, No. 4, 1999, pp. 873-907. doi:10.1111/1467-937X.00112

[8] D. Hudgins and C. Chan, “Optimal Exchange Rate Policy under Unknown Pass-Through and Learning with Applications to Korea,” Computational Economics, Vol. 32, No. 3, 2008, pp. 279-293. doi:10.1007/s10614-008-9139-1

[9] L. Hansen and T. Sargent, “Robustness,” Princeton University Press, New York, 2008.

[10] P. Bernhard, “Survey of Linear Quadratic Robust Control,” Macroeconomic Dynamics, Vol. 6, No. 1, 2002, pp. 19-39. doi:10.1017/S1365100502027037

[11] R. Dennis, K. Leitemo and U. Soderstrom, “Methods for Robust Control,” Journal of Economic Dynamics and Control, Vol. 33, No. 8, 2009, pp. 1004-1616. doi:10.1016/j.jedc.2009.02.011

[12] G. Barlevy, “Robustness and Macroeconomic Policy,” Annual Review of Economics, Federal Reserve Bank of Chicago, Vol. 3, No. 1, 2011, pp. 1-24.

[13] T. Basar and G. Olsder, “Dynamic Noncooperative Game Theory,” Academic Press, London, 1982.

[14] D. Luenberger, “Introduction to Dynamic Systems,” John Wiley & Sons, New York, 1979.

[15] F. Lewis, “Optimal Control,” John Wiley & Sons, New York, 1986.

[16] Z. Pan and T. Basar, “Designing H∞-Optimal Controllerfor Singularly Perturbed Systems; Part I: Perfect State Measurements,” Automatica, Vol. 29, No. 2, 1991, pp. 401-423. doi:10.1016/0005-1098(93)90132-D

[1] T. Basar and P. Bernhard, “H∞-Optimal Control and Related Minimax Design Problems,” Birkhauser, Boston, 1991.

[2] G. Chow, “Analysis and Control of Dynamic Economic Systems,” John Wiley and Sons, New York, 1975.

[3] A. Sage and C. White, “Optimum Systems Control,” 2nd Edition, E Prentice Hall, Engelwood Cliffs, 1977.

[4] D. Kendrick, “Stochastic Control for Econometric Models,” McGraw Hill, New York, 1981.

[5] A. Tornell, “Robust-H-Infinity Forecasting and Asset Pricing Anomalies,” NBER Working Paper No. 7753, 2000.

[6] T. Basar, “On the Application of Differential Game Theory in Robust Controller Design for Economic Systems,” In: G. Feichtinger, Ed., Dynamic Economic Models and Optimal Control, North-Holland, Amsterdam, 1992, pp. 269-278.

[7] L. Hansen, T. Sargent and T. Tallarini, “Robust Permanent Income and Pricing,” Review of Economic Studies, Vol. 66, No. 4, 1999, pp. 873-907. doi:10.1111/1467-937X.00112

[8] D. Hudgins and C. Chan, “Optimal Exchange Rate Policy under Unknown Pass-Through and Learning with Applications to Korea,” Computational Economics, Vol. 32, No. 3, 2008, pp. 279-293. doi:10.1007/s10614-008-9139-1

[9] L. Hansen and T. Sargent, “Robustness,” Princeton University Press, New York, 2008.

[10] P. Bernhard, “Survey of Linear Quadratic Robust Control,” Macroeconomic Dynamics, Vol. 6, No. 1, 2002, pp. 19-39. doi:10.1017/S1365100502027037

[11] R. Dennis, K. Leitemo and U. Soderstrom, “Methods for Robust Control,” Journal of Economic Dynamics and Control, Vol. 33, No. 8, 2009, pp. 1004-1616. doi:10.1016/j.jedc.2009.02.011

[12] G. Barlevy, “Robustness and Macroeconomic Policy,” Annual Review of Economics, Federal Reserve Bank of Chicago, Vol. 3, No. 1, 2011, pp. 1-24.

[13] T. Basar and G. Olsder, “Dynamic Noncooperative Game Theory,” Academic Press, London, 1982.

[14] D. Luenberger, “Introduction to Dynamic Systems,” John Wiley & Sons, New York, 1979.

[15] F. Lewis, “Optimal Control,” John Wiley & Sons, New York, 1986.

[16] Z. Pan and T. Basar, “Designing H∞-Optimal Controllerfor Singularly Perturbed Systems; Part I: Perfect State Measurements,” Automatica, Vol. 29, No. 2, 1991, pp. 401-423. doi:10.1016/0005-1098(93)90132-D