Step | Mean of | Standard deviation of | Mean of loss | Standard deviation of loss |
500 | 0.4643 | 9.58E-2 | 8.46E-2 | 1.27E-1 |
1000 | 0.4136 | 2.55E-2 | 7.13E-3 | 1.23E-2 |
2000 | 0.3972 | 1.21E-3 | 8.47E-4 | 6.23E-4 |
3000 | 0.3972 | 3.69E-4 | 5.80E-4 | 3.20E-4 |
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration. This posterior estimate validates the convergence of the recently proposed Deep BSDE method. In addition, we developed a numerical scheme based on the Deep BSDE method and presented numerical examples in financial markets to demonstrate the high performance.
Citation: |
Table 1. Numerical simulation of CIR bond
Step | Mean of | Standard deviation of | Mean of loss | Standard deviation of loss |
500 | 0.4643 | 9.58E-2 | 8.46E-2 | 1.27E-1 |
1000 | 0.4136 | 2.55E-2 | 7.13E-3 | 1.23E-2 |
2000 | 0.3972 | 1.21E-3 | 8.47E-4 | 6.23E-4 |
3000 | 0.3972 | 3.69E-4 | 5.80E-4 | 3.20E-4 |
Table 2. Numerical simulation of multi-dimensional CIR bond
Step | Mean of | Standard deviation of | Mean of loss | Standard deviation of loss |
500 | 0.3773 | 8.77E-2 | 1.15E-1 | 1.66E-1 |
1000 | 0.3228 | 2.03E-2 | 5.51E-3 | 8.33E-3 |
2000 | 0.3100 | 1.63E-3 | 4.50E-4 | 1.12E-4 |
3000 | 0.3095 | 8.28E-4 | 3.89E-4 | 7.20E-5 |
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Relative error of the bond price (left) and the loss (right) against the number of the iteration steps
Relative error of the bond price under multi-dimensional CIR model (left) and the loss (right) against the number of the iteration steps