Financial signal processing : applications to asset-market dynamics and healthcare finance

Abstract

The seemingly random fluctuations of price and value produced by information flow and complex interactions across a diverse population of stakeholders has motivated the extensive use of stochastic processes to analyze both capital markets and the regulatory approval process in healthcare. This thesis approaches the statistical analysis of such processes through the lens of signal processing, with a particular emphasis on studying how dynamics evolve over time. We begin with a brief introduction to financial signal processing in Part I, before turning to specific applications in the main body of the thesis. In Part II, we apply spectral analysis to understand and quantify the relationship between asset-market dynamics across multiple time horizons, and show how this framework can be used to improve portfolio and risk management. Using the Fourier transform, we decompose asset-return alphas, betas and covariances into distinct frequency components, allowing us to identify the relative importance of specific time horizons in determining each of these quantities. Our approach can be applied to any portfolio, and is particularly useful for comparing the forecast power of multiple investment strategies. Part III addresses the growing interest from the healthcare industry, regulators and patients to include Bayesian adaptive methods in the regulatory approval process of new therapies. By applying sequential likelihood ratio tests to a Bayesian decision analysis framework that assigns asymmetric weights to false approvals and false rejections, we are able to design adaptive clinical trials that maximize the value to current and future patients and consequently, public health. We also consider the possibility that as the process unfolds, drug sponsors might stop a trial early if new information suggests market prospects are not as favorable as originally forecasted. We show that clinical trials that can be modified as data are observed are more valuable than trials without this flexibility.