Query algorithms are everywhere. Gradient Descent is a well-known algorithm that queries the gradient of a hidden function and moves towards the minimum of the function.

Abstract: Mathematical proofs when written in conventional ways often contain imprecise definitions, unstated background assumptions, and inferential gaps in reasoning.

Abstract:  In this thesis, we develop computational algorithms in a number of different regimes for pricing financial American options.

Change of measure techniques are ubiquitous in many areas of applied probability including in model selection in finance and in efficient simulation of rare events.