We present an introduction to mathematical Finance Theory for mathematicians. The approach is to start with an abstract setting and then introduce hypotheses as needed to develop the theory. We present the basics of European call and put options, and we show the connection between American put...

Discretely sampled variance and volatility swaps trade actively in OTC markets. To price these swaps, the continuously sampled approximation is often used to simplify the computations. The purpose of this paper is to study the conditions under which this approximation is valid. Our first set of...

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via...