Multidisciplinary essays on finance

This thesis includes four studies which, in the broadest sense, fall within the finance domain. The first chapter studies stochastic processes from a mathematical finance perspective, and more specifically develops theorems for regime switching. Chapter two develops a framework for the analysis of scenarios from an economic perspective, conditional on forward looking information. Chapter three takes a corporate finance angle and describes the optimization of the external audit using belief functions. Finally, the last chapter introduces a statistical test for partial monotonicity that can be useful in a data science approach to financial research problems.