Ruimeng Hu (UCSB)

Title: Global Ranking Problems, Sequential Design and Applications to Real Options

Abstract: We consider sequential design approaches to the problem of determining the pointwise index of the smallest function among a family of N functions f_i(x), i = 1, 2, ..., N, over a multi-dimensional domain X. The f_i’s are unknown but can be noisily sampled. In other words, our main goal is to identify the index corresponding to the minimal surface globally over X. It is related to the classical regression problem, but not the same. Our context is motivated by the extension of the sequential Regression Monte Carlo approach to optimal switching problems. A 1D example with N = 2 is studied, and applications to valuation of real options for irreversible capacity expansion will also be presented.