A deep primal-dual BSDE method for optimal stopping problems
ArXiv ID: 2409.06937 “View on arXiv”
Authors: Unknown
Abstract
We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which consists of subnetwork parameterization of a continuation value and spatial gradients from present up to the stopping time. Notable features of the method include: (i) The martingale part in the loss function reduces the variance of stochastic gradients, which facilitates the training of the neural networks as well as alleviates the error propagation of value function approximation; (ii) this martingale approximates the martingale in the Doob-Meyer decomposition, and thus leads to a true upper bound for the optimal value in a non-nested Monte Carlo way. We test the proposed method in American option pricing problems, where the spatial gradient network yields the hedging ratio directly.
Keywords: Deep Primal-Dual BSDE, Optimal Stopping, American Options, Monte Carlo Methods, Neural Networks, Equity Derivatives
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 7.0/10
- Quadrant: Holy Grail
- Why: The paper presents advanced stochastic calculus and BSDE theory with complex loss function derivations, while also detailing specific implementation (stopping time iteration, neural networks, variance reduction) and validating on multiple finance problems (American options, Heston model).
flowchart TD
A["Research Goal<br>Develop a deep primal-dual BSDE method<br>for optimal stopping problems"]
B["Methodology"]
C["Data & Input<br>Underlying asset paths<br>Payoff function"]
D["Computational Process<br>Deep Neural Networks<br>BSDE Iteration<br>Loss Function Optimization"]
E["Key Findings & Outcomes<br>True Upper Bound on Optimal Value<br>Hedging Ratio Calculation<br>Reduced Variance in Training"]
A --> B
A --> C
B --> D
C --> D
D --> E