We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measu...

Optimal stopping is a sub-field of probability theory that is present within mathematical finance, mathematical statistics, stochastic calculus and other disciplines. In mathematical finance, one well known problem is the pricing of an American put option. In this thesis we first give a brief review of some general optimal stopping theory, its connection to free-boundary problems and we then ex...

We study the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the bid-ask prices of vanilla call options in the underlying securities. We show that this semi-infinite problem can be recast as a linear program whose size is linear in the input data size. These developments advance previous related results, and enhance the practical va...