Adversarial Robust Deep Hedging

Objective

This repository solves problems of the type:

Maximize

$$ \inf_{P}R\Big(\sum_{n = 0}^{N-1} \phi_{t_n} \Delta S_{t_{n+1}}^P - C_{t_N}\Big) + \alpha(P) $$

where

• $P$ is a measure implying the dynamics of
• a stock $S$ that
• can be traded on times $t_0, ..., t_{N-1}$
• with the strategy $\phi_{t_n}$ over the increment $\Delta S_{t_{n+1}} := S_{t_{n+1}} - S_{t_n}$ for all $n \in \lbrace 0, ..., N-1\rbrace$ to
• replicate an option with terminal payoff $C_{t_N}$

This should then maximize

• a utility functional $R$, which is
• penalized by $\alpha(P$), a penalty which is necessarily characterized as the function of the Sig-Wasserstein-distance of $P$ to some reference measure $Q$.

Structure

The repository contains three core modules,

• generation
• deep_hedging
• penalty

mimicking the three tasks that are united to solve problems as outlined above.

Another module, gan focuses on the interplay of the three mentioned modules and provides the machinery for training procedures.

An overview of the architecture provided in the Structure.puml, which yields: