Efficient state estimation strategies for stochastic optimal control of financial risk problems

Yue Yuin Lim; Sie Long Kek; Kok Lay Teo; Yue Yuin Lim; Sie Long Kek; Kok Lay Teo

doi:10.3934/DSFE.2022018

Data Science in Finance and Economics

2022, Volume 2, Issue 4: 356-370. doi: 10.3934/DSFE.2022018

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Research article

Efficient state estimation strategies for stochastic optimal control of financial risk problems

1.
Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, 84600 Pagoh, Muar, Johor Darul Takzim, Malaysia
2.
School of Mathematical Sciences, Sunway University, Bandar Sunway, 47500 Selangor Darul Ehsan, Malaysia
3.
Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China

Received: 06 August 2022 Revised: 28 September 2022 Accepted: 05 October 2022 Published: 17 October 2022
JEL Codes: C13, C32, C53, C61, G32

In this paper, a financial risk model, which is formulated from the risk management process of financial markets, is studied. By considering the presence of Gaussian white noise, the financial risk model is reformulated as a stochastic optimal control problem. On this basis, two efficient computational approaches for state estimation, which are the extended Kalman filter (EKF) and unscented Kalman filter (UKF) approaches, are applied. Later, based on the state estimate given by the EKF and UKF approaches, a linear feedback control policy is designed from the stationary condition. For illustration, some parameter values and the initial conditions of the financial risk model are used for the simulation of the stochastic optimal control problem. From the results, it is noticed that the UKF algorithm provides a better state estimate with a smaller value of the sum of squared errors (SSE) as compared to the SSE given by the EKF algorithm. Thus, the estimated output trajectory has a high accuracy that is close to the real output. Moreover, the control effort assists in estimating the state dynamics at the minimum cost. In conclusion, the efficiency of the computational approaches for optimal control of the financial risk model has been well presented.
- financial risk,
- stochastic optimal control,
- state estimation,
- Kalman filter,
- control law design
Citation: Yue Yuin Lim, Sie Long Kek, Kok Lay Teo. Efficient state estimation strategies for stochastic optimal control of financial risk problems[J]. Data Science in Finance and Economics, 2022, 2(4): 356-370. doi: 10.3934/DSFE.2022018

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Abstract

In this paper, a financial risk model, which is formulated from the risk management process of financial markets, is studied. By considering the presence of Gaussian white noise, the financial risk model is reformulated as a stochastic optimal control problem. On this basis, two efficient computational approaches for state estimation, which are the extended Kalman filter (EKF) and unscented Kalman filter (UKF) approaches, are applied. Later, based on the state estimate given by the EKF and UKF approaches, a linear feedback control policy is designed from the stationary condition. For illustration, some parameter values and the initial conditions of the financial risk model are used for the simulation of the stochastic optimal control problem. From the results, it is noticed that the UKF algorithm provides a better state estimate with a smaller value of the sum of squared errors (SSE) as compared to the SSE given by the EKF algorithm. Thus, the estimated output trajectory has a high accuracy that is close to the real output. Moreover, the control effort assists in estimating the state dynamics at the minimum cost. In conclusion, the efficiency of the computational approaches for optimal control of the financial risk model has been well presented.

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