# Neural network approximation for superhedging prices

@inproceedings{Biagini2021NeuralNA, title={Neural network approximation for superhedging prices}, author={Francesca Biagini and Lukas Gonon and Thomas Reitsam}, year={2021} }

This article examines neural network-based approximations for the superhedging price process of a contingent claim in a discrete time market model. First we prove that the α-quantile hedging price converges to the superhedging price at time 0 for α tending to 1, and show that the α-quantile hedging price can be approximated by a neural network-based price. This provides a neural network-based approximation for the superhedging price at time 0 and also the superhedging strategy up to maturity… Expand

#### References

SHOWING 1-10 OF 28 REFERENCES

Robust Estimation of Superhedging Prices

- Mathematics
- 2018

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and… Expand

Duality for pathwise superhedging in continuous time

- Mathematics, Economics
- Finance and Stochastics
- 2019

We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of d$d$ risky assets with continuous price trajectories, we show that the purely analytic… Expand

A class of financial products and models where super-replication prices are explicit

- Economics
- 2006

AbstractWe consider a multidimensional financial model with mild conditions on the underlying asset price process. The trading is only allowed at some fixed discrete times and the strategy is… Expand

Deep Hedging

- Economics, Mathematics
- 2018

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep… Expand

Neural Networks for Option Pricing and Hedging: A Literature Review

- Economics, Computer Science
- ArXiv
- 2019

This note intends to provide a comprehensive review of neural networks as a nonparametric method for option pricing and hedging since the early 1990s in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Expand

Robust pricing–hedging dualities in continuous time

- Mathematics, Computer Science
- Finance Stochastics
- 2018

A robust approach to pricing and hedging in mathematical finance is pursued and a general pricing–hedging duality result is obtained: the infimum over superhedging prices of an exotic option with payoff G$G$ is equal to the supremum of expectations of expectations under calibrated martingale measures. Expand

Model-free superhedging duality

- Mathematics, Economics
- 2015

In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the… Expand

HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12

- Economics
- 1996

We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be… Expand

Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market

- Mathematics
- 1995

The problem of pricing contingent claims or options from the price dynamics of certain securities is well understood in the context of a complete financial market. This paper studies the same problem… Expand

Pathwise superhedging on prediction sets

- Mathematics, Economics
- 2017

In this paper, we provide a pricing–hedging duality for the model-independent superhedging price with respect to a prediction set Ξ ⊆ C [ 0 , T ] $\Xi \subseteq C[0,T]$ , where the superhedging… Expand