A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs
Abstract
1. Introduction
2. Problem Description and Method
2.1. Formulation of the Optimal Trading Problem
2.2. Bounds of the Value Functions
2.3. The HJB Equations
2.4. Solutions of the HJB Equations
2.5. A Verification Theorem
3. Numerical Results and Discussion
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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b | 1 | 1.5 | 2 | 2.5 | 3 |
---|---|---|---|---|---|
−4.36 | −4.46 | −4.58 | −4.66 | −4.74 | |
0 | 0.64 | 1.22 | 1.78 | 2.34 | |
0.74 | 1.22 | 1.7 | 2.18 | 2.66 |
a | 0.6 | 0.7 | 0.8 | 0.9 | 1 |
---|---|---|---|---|---|
−4.2 | −4.4 | −4.58 | −4.72 | −4.86 | |
0.98 | 1.14 | 1.22 | 1.3 | 1.36 | |
1.58 | 1.62 | 1.7 | 1.74 | 1.78 |
0.3 | 0.4 | 0.5 | 0.6 | 0.7 | |
---|---|---|---|---|---|
−4.56 | −4.56 | −4.58 | −4.58 | −4.6 | |
1.12 | 1.16 | 1.22 | 1.28 | 1.36 | |
1.54 | 1.62 | 1.7 | 1.8 | 1.9 |
0.3 | 0.4 | 0.5 | 0.6 | 0.7 | |
---|---|---|---|---|---|
−5 | −4.86 | −4.58 | −4.32 | −4.12 | |
1.56 | 1.36 | 1.22 | 1.06 | 0.9 | |
1.94 | 1.84 | 1.7 | 1.56 | 1.42 |
K | 0.01 | 0.05 | 0.1 | 0.5 | 1 |
---|---|---|---|---|---|
−5 | −5 | −4.58 | −2.56 | −1.6 | |
1.46 | 1.3 | 1.22 | 0.7 | −0.46 | |
1.56 | 1.68 | 1.7 | 1.78 | 1.86 |
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Luu, P.; Tie, J.; Zhang, Q. A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs. Risks 2018, 6, 107. https://doi.org/10.3390/risks6040107
Luu P, Tie J, Zhang Q. A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs. Risks. 2018; 6(4):107. https://doi.org/10.3390/risks6040107
Chicago/Turabian StyleLuu, Phong, Jingzhi Tie, and Qing Zhang. 2018. "A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs" Risks 6, no. 4: 107. https://doi.org/10.3390/risks6040107
APA StyleLuu, P., Tie, J., & Zhang, Q. (2018). A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs. Risks, 6(4), 107. https://doi.org/10.3390/risks6040107