Date of Award

May 2019

Degree Type

Thesis

Degree Name

Master of Science

Department

Mathematics

First Advisor

Chao Zhu

Committee Members

Chao Zhu, Wei Wei, Richard H Stockbridge

Keywords

Convex Risk Measures, Financial Mathematics, Machine Learning, Neural Networks, Pricing and Hedging of Derivatives

Abstract

Inspired by the recent paper Buehler et al. (2018), this thesis aims to investigate the optimal hedging and pricing of financial derivatives with neural networks. We utilize the concept of convex risk measures to define optimal hedging strategies without strong assumptions on the underlying market dynamics. Furthermore, the setting allows the incorporation of market frictions and thus the determination of optimal hedging strategies and prices even in incomplete markets. We then use the approximation capabilities of neural networks to find close-to optimal estimates for these strategies.

We will elaborate on the theoretical foundations of this approach and carry out implementations and a detailed analysis of the method with simulated market data.

Our experiments show that the neural network-based algorithm is a powerful tool for the model-independent pricing of any financial derivative and the estimation of optimal hedging strategies for these instruments.

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