Introduction

Abstract

This chapter introduces the industry context for machine learning in finance, discussing the critical events that have shaped the finance industry’s need for machine learning and the unique barriers to adoption. The finance industry has adopted machine learning to varying degrees of sophistication. How it has been adopted is heavily fragmented by the academic disciplines underpinning the applications. We view some key mathematical examples that demonstrate the nature of machine learning and how it is used in practice, with the focus on building intuition for more technical expositions in later chapters. In particular, we begin to address many finance practitioner’s concerns that neural networks are a “black-box” by showing how they are related to existing well-established techniques such as linear regression, logistic regression, and autoregressive time series models. Such arguments are developed further in later chapters. This chapter also introduces reinforcement learning for finance and is followed by more in-depth case studies highlighting the design concepts and practical challenges of applying machine learning in practice.

Appendix

1.1 I Answers to Multiple Choice Questions

Question 1

Answer: 1, 2.

Answer 3 is incorrect. While it is true that unsupervised learning does not require a human supervisor to train the model, it is false to presume that the approach is superior.

Answer 4 is incorrect. Reinforcement learning cannot be viewed as a generalization of supervised learning to Markov Decision Processes. The reason is that reinforcement learning uses rewards to reinforce decisions, rather than labels to define the correct decision. For this reason, reinforcement learning uses a weaker form of supervision.

Question 2

Answer: 1,2,3.

Answer 4 is incorrect. Two separate binary models $\{g^{(1)}_i(X | \theta )\}_{i=0}^{1}$ and $\{g^{(2)}_i(X | \theta )\}_{i=0}^{1}$ will, in general, not produce the same output as a single, multi-class, model $\{g_i(X | \theta )\}_{i=0}^{3}$. Consider, as a counter example, the logistic models $g^{(1)}_0=g_0(X | \theta _1)=\frac {\exp \{-X^T\theta _1\}}{1+ \exp \{-X^T\theta _1\}}$ and $g^{(2)}_0=g_0(X | \theta _2)=\frac {\exp \{-X^T\theta _2\}}{1+ \exp \{-X^T\theta _2\}}$, compared with the multi-class model

$$\displaystyle \begin{aligned} g_i(X | \boldsymbol{\theta}')=\text{softmax}(\exp\{X^T\boldsymbol{\theta}'\})=\frac{\exp\{(X^T\boldsymbol{\theta}')_i\}}{\sum_{k=0}^K\exp\{(X^T\boldsymbol{\theta}')_k\}}. \end{aligned} $$

(1.26)

If we set $\theta _1=\boldsymbol {\theta }^{\prime }_0-\boldsymbol {\theta }^{\prime }_1$ and $\boldsymbol {\theta }^{\prime }_2= \boldsymbol {\theta }^{\prime }_3=0$, then the multi-class model is equivalent to Model 1. Similarly if we set $\theta _2=\boldsymbol {\theta }^{\prime }_2-\boldsymbol {\theta }^{\prime }_3$ and $\boldsymbol {\theta }^{\prime }_0= \boldsymbol {\theta }^{\prime }_1=0$, then the multi-class model is equivalent to Model 2. However, we cannot simultaneously match the outputs of Model 1 and Model 2 with the multi-class model.

Question 3

Answer: 1,2,3.

Answer 4 is incorrect. The layers in a deep recurrent network provide more expressibility between each lagged input and the hidden state variable, but are unrelated to the amount of memory in the network. The hidden layers in any multilayered perceptron are not the hidden state variables in our time series model. It is the degree of unfolding, i.e. number of hidden state vectors which determines the amount of memory in any recurrent network.

Question 4

Answer: 2.