Document Type

Thesis

Degree Name

Master of Science (MSc)

Department

Mathematics

Program Name/Specialization

Mathematics for Science and Finance

Faculty/School

Faculty of Science

First Advisor

Xu (Sunny) Wang

Advisor Role

Supervisor

Abstract

Hawkes process was evolved so that the past events contribute to the occurrence time of future events by self-exciting or mutually exciting. However, many real-world data do not follow the Hawkes process's assumptions (i.e., positivity, additivity, and exponential decay) and become more complex to be modeled by the traditional Hawkes processes, so the neural Hawkes process was developed to tackle the challenges. However, Recurrent Neural Networks (RNN) fail to capture long-term dependencies among multiple point processes, and Transformer Hawkes processes only address temporal characteristics of Hawkes processes. In this thesis, we proposed a combination of neural networks and Hawkes processes to tackle the aforementioned challenges and to capture contagious effects among different points processes. First, we made substantial modifications to the Transformer Hawkes process by utilizing two encoders, which include two Multi-Head attention modules: 1) event significance attention and 2) temporal attention. Then, to improve this model, the Modern Hopfield Neural Network was incorporated to better assign the attention to the test set by appending the decoder layer to the previous modified encoder layers. Credit Default Swap data for ten European countries were tested, and the results revealed that modeling the contagious effect ameliorates the prediction performance.

Convocation Year

2021

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