Deep learning for ranking response surfaces with applications to optimal stopping problems

@article{Hu2019DeepLF,
  title={Deep learning for ranking response surfaces with applications to optimal stopping problems},
  author={Ruimeng Hu},
  journal={Quantitative Finance},
  year={2019},
  volume={20},
  pages={1567 - 1581}
}
  • Ruimeng Hu
  • Published 2019
  • Computer Science, Mathematics, Economics
  • Quantitative Finance
In this paper, we propose deep learning algorithms for ranking response surfaces with applications to optimal stopping problems in financial mathematics. The problem of ranking response surfaces is motivated by estimating optimal feedback policy maps in stochastic control problems, aiming to efficiently find the index associated with the minimal response across the entire continuous input space . By considering points in as pixels and indices of the minimal surfaces as labels, we recast the… Expand
Deep Reinforcement Learning for Optimal Stopping with Application in Financial Engineering
TLDR
This paper presents for the first time a comprehensive empirical evaluation of the quality of optimal stopping policies identified by three state of the art deep RL algorithms: double deep Q-learning (DDQN), categorical distributional RL (C51), and Implicit Quantile Networks (IQN). Expand
Deep Fictitious Play for Stochastic Differential Games
TLDR
The idea of fictitious play is applied to design deep neural networks (DNNs), and deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N-player non-zero-sum stochastic differential games are developed. Expand
Research on financial assets transaction prediction model based on LSTM neural network
TLDR
It is proved that the LSTM deep neural network has higher prediction accuracy and can effectively predict the stock market time series. Expand
Research on Crisis Warning Model of Enterprise Finance Based on Deep Learning
Looking for an effective financial crisis early warning method is of great significance to China's economy and company development. This paper fully considers the internal factors that affect theExpand
Convergence of Deep Fictitious Play for Stochastic Differential Games
TLDR
Under appropriate conditions, the convergence of deep fictitious play (DFP) to the true Nash equilibrium is proved, and it is shown that the strategy based on DFP forms an $\epsilon$-Nash equilibrium. Expand

References

SHOWING 1-10 OF 71 REFERENCES
Sequential Design for Ranking Response Surfaces
TLDR
This work proposes and analyzes sequential design methods for the problem of ranking several response surfaces over a continuous input space and investigates stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. Expand
Sequential Design for Optimal Stopping Problems
TLDR
Adapt generation of the stochastic grids anchoring the simulated sample paths of the underlying state process allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. Expand
Dynamic Trees for Learning and Design
TLDR
A sequential tree model whose state changes in time with the accumulation of new data is created, and particle learning algorithms that allow for the efficient online posterior filtering of tree states are provided. Expand
A mean-field optimal control formulation of deep learning
TLDR
This paper introduces the mathematical formulation of the population risk minimization problem in deep learning as a mean-field optimal control problem, and state and prove optimality conditions of both the Hamilton–Jacobi–Bellman type and the Pontryagin type. Expand
Deep Optimal Stopping
TLDR
A deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples is developed, broadly applicable in situations where the underlying randomness can efficiently be simulated. Expand
Adam: A Method for Stochastic Optimization
TLDR
This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Expand
Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation
TLDR
This work investigates Gaussian process (GP) metamodels, and analyzes several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. Expand
X-Armed Bandits
We consider a generalization of stochastic bandits where the set of arms, X, is allowed to be a generic measurable space and the mean-payoff function is "locally Lipschitz" with respect to aExpand
A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension
TLDR
A probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon is presented. Expand
Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models
TLDR
Two efficient techniques which allow one to compute the price of American basket options, called GPR Tree and GPR Exact Integration, are proposed, which solve the backward dynamic programing problem considering a Bermudan approximation of the American option. Expand
...
1
2
3
4
5
...