Основные понятия
Proposing a GAN approach for robust utility optimization in realistic market settings.
Аннотация
The article introduces a generative adversarial network (GAN) approach to solve robust utility optimization problems in general and realistic settings. It models both the investor and the market by neural networks, training them in a mini-max zero-sum game. The method is applicable for any continuous utility function and in realistic market settings with trading costs. The study shows that the trained path-dependent strategies do not outperform Markovian ones and uncovers universally applicable alternatives to well-known asymptotic strategies of idealized settings.
- Introduction:
- Uncertainty in financial markets necessitates robust utility optimization.
- Balancing returns and risk is crucial for rational decision-making.
- Robust utility maximization involves a zero-sum game between trader and market.
- Preliminaries:
- Financial market model with risky assets and risk-free rate considered.
- Agent trades using portfolio weights, dynamics governed by asset values.
- Robust portfolio optimization problem formulated as a min-max game.
- Deep Robust Utility Optimization:
- Discrete-time market setting introduced for approximating solutions.
- GAN-based algorithm proposed for approximating solutions under constraints.
- Training process outlined with generator and discriminator networks.
- Experiments:
- Various scenarios tested, including friction-less settings with analytic solutions.
- Performance evaluated against optimal strategies, showing promising results.
- Impact of transaction costs analyzed, demonstrating improved performance with higher costs.
- Evaluation Criterion:
- Metrics proposed to assess robustness and quality of trained models.
- Early stopping criteria based on reference market models implemented.
Статистика
In this work, we propose a generative adversarial network (GAN) approach to (approximately) solve robust utility optimization problems in general and realistic settings.
Whenever an optimal reference strategy is available, our method performs on par with it...
With advances in deep learning (DL), new techniques have been developed for solving control problems under entirely general constraints...
For these sorts of problems, generative adversarial network (GAN) approaches seem particularly well suited...
Through robust approaches, GANs have progressed into mathematical finance as well...
For simplicity, we speak of the GAN approach or GAN strategies even if we fix the market dynamics...
One major advantage of the GAN approach to (robust) utility optimization is that it is universally applicable across choices of utility functions...
We empirically show that the GAN approaches successfully recover the optimal strategies in multi-asset, friction-less markets with log utilities...
Our model achieves a very small relative error compared to the analytic solution π∗ satisfying errΣ⋆,µ rel(πNN, π⋆) < 0.2%...
In all cases, our model achieves a very small relative error compared to the analytic solution π∗ satisfying errΣ⋆,µ rel(πNN, π⋆) < 0.2%...
We consider various stock market settings with different levels of transaction costs...
Since no analytic solution is known...
Based on the reference model...
Noisy Market Models around Reference Market: We generate random noisy market scenarios Σnoisy,j t , µnoisy,j t ...
Constant noise: For each j we sample one realization from normal distributions...
Non-constant noise: For each j and t we sample one realization from normal distributions...
Cumulative noise: For each j we sample a Brownian motion path starting at ˜Σ...
Цитаты
"In particular, this allows us to apply our method to the problem of optimal investment under transaction costs..."
"Our model achieves a very small relative error compared to the analytic solution..."
"We consider various stock market settings with different levels of transaction costs..."