Trajectory Based Market Models for Two Stocks

This paper studies the explicit calculation of the set of superhedging (and underhedging) portfolios where one asset is used to superhedge another in a discrete time setting. A general operational framework is proposed and trajectory models are defined based on a class of investors characterized by how they operate on financial data leading to potential portfolio rebalances. Trajectory market models will be specified by a trajectory set and a set of portfolios. Beginning with observing charts in an operationally prescribed manner, our trajectory sets will be constructed by moving forward recursively, while our superhedging portfolios are computed through a backwards recursion process involving a convex hull algorithm. The models proposed in this thesis allow for an arbitrary number of stocks and arbitrary choice of numeraire. Although price bounds, V 0 (X0, X2 ,M) ≤ V 0(X0, X2 ,M), will never yield a market misprice, our models will allow an investor to determine the amount of risk associated with an initial investment v.