Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from...

In this paper we develop a new notion of convergence for discussing the relationship between discrete and continuous financial models, "D"-super-2-convergence. This is stronger than weak convergence, the commonly used mode of convergence in the finance literature. We show that...

The integrand, when a martingale under an equivalent measure is represented as a stochastic integral, is determined by elementary methods in the Markov situation. Applications to hedging portfolios in finance are described.