Lim, Yue Yuin (2022) Developing algorithms and comparing filtering techniques for three stochastic optimal control problems in finance. Masters thesis, Universiti Tun Hussein Onn Malaysia.

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Abstract

Optimization and control of a nonlinear dynamical system that is disturbed by random noises is a challenging task. In this thesis, the application of Kalman filtering techniques is aimed at solving stochastic optimal control problems in economics and finance. For this purpose, the extended Kalman filter for state-control (EKFSC) and unscented Kalman filter for state-control (UKFSC) algorithms are developed to associate state estimation and optimal control law. In the EKFSC algorithm, the state equation is propagated and linearized. Then, the updates on output measurement and time are taken to estimate the state dynamics. While, in the UKFSC algorithm, the unscented transform is applied to the state equation so that a set of sigma points is generated. Based on these sigma points, the state dynamics are predicted through updating output measurement and time. By applying the state estimates, the optimal control law is designed properly. Here, the state estimate and the optimal control are assumed to follow the principle of separation. For illustration, three stochastic optimal control problems, which are economic growth, financial risk, and chaotic and hyperchaotic financial models, are studied. The simulation results showed that the state dynamics of these models are well-estimated by the UKFSC algorithm with a smaller mean square error than the EKFSC algorithm. Furthermore, these dynamic systems using the UKFSC algorithm achieve better stability, and better optimal solutions than the EKFSC algorithm. In conclusion, the efficiency of the UKFSC algorithm for handling nonlinear stochastic optimal control problems in economics and finance is verified appropriately

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