Research article

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

  • 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.

    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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  • 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.



    Biomedical and health information processing and analysis is playing an increasingly important role in life sciences and medicine. Relevant technologies are developing rapidly and help to assess surgical risks, process electronic medical records (EMR) or medical images, and provide precision medicine. This special issue aims to present some research about the application of medical data mining, and bioinformatics in processing or analyzing biomedical and health information.

    There are 7 full length articles in this special issue. All articles are focused on medical data mining and bioinformatics.

    Wan et al. [1] proposed a ELMo-ET-CRF model to extract medical named entities from Chinese EMR. The model used a Chinese medical domain-specific pretrained ELMo model as embedding layer, an encoder from transformer (ET) as encoding layer, conditional random field (CRF) as decoding layer, respectively. The model achieved competitive performance to the current state-of-the-art method on CCKS 2019 datasets.

    Che et al. [2] integrated temporal convolutional network (TCN) and CRF for biomedical named entity recognition. The model significantly reduced training time while achieved comparable performance to the state-of-the-art methods on GENIA and CoNLL-2003 datasets.

    Based on a pre-trained language model, Zhang et al. [3] presented a novel encoder-decoder structure for Chinese clinical event detection. The structure integrated contextual representations and character embeddings to improve semantic understanding. The experiments demonstrated the novel structure achieved the best precision, recall and F1-score.

    Cheng et al. [4] optimized the U-Net for retinal blood vessel segmentation by adding dense blocks. This optimization improved the sensitivity of small blood vessels and outperformed state-of-the-art methods on two public datasets DRIVE and CHASE_DB1.

    Liu et al. [5] proposed four methods, namely SESOP, STSSO, SESOP-MFIR and STSSO-MFIR, for the surgical outcome monitoring. The methods were optimized by standardizing variables, replacing statistics, and upgrading the control limits from asymptotic to time-varying. The experiments showed that the methods could effectively monitor surgical outcomes and early shifts.

    Zhang et al. [6] proposed an anomaly detection method based on local density. By integrating with homomorphic encryption, the method could effectively and efficiently perform anomaly detection in the case of multi-party participation without leaking the private data of participants.

    Hou et al. [7] developed a knowledge representation model named precision medicine ontology (PMO) to represent the relationships among 11 fields related to precision medicine, such as diseases, phenotypes, genes, mutations, drugs, etc., in 93 semantic relationships. Compared with the existing work, PMO covered mutations, genes and gene products more extensively, and had richer term set including 4.53 million terms.

    In conclusion, this special issue provides 7 outstanding full-length research articles, mainly about the application of medical data mining, and bioinformatics in processing or analyzing biomedical and health information. We sincerely express our gratitude to all researchers who accepted our invitation and contributed to this special issue. In addition, we also thank MBE for editing assistance.

    The work is supported by Natural Science Foundation of China (No. 61772146 and No. 61672450) and Guangzhou Science Technology and Innovation Commission (No. 201803010063).

    The authors declare that they have no conflict of interest.



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