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 in both capital markets and regulatory decision-making 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.
In Part I, 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 II addresses the growing interest from the healthcare industry, regulators and patients to include Bayesian adaptive methods in the regulatory-approval process of new therapies. We apply sequential likelihood ratio tests to design adaptive randomized clinical trials that maximize expected value to current and future patients, as well as to industry sponsors of new therapies. We show that clinical trials that can be modified as new data are observed are more valuable than trials without this flexibility.
Thesis Committee: Andrew Lo (MIT; Sloan; CSAIL), John Guttag (MIT; CSAIL), Leonid Kogan (MIT; Sloan)