ABSTRACT
Revisit the one-step, multistate discrete financial model described by a market matrix and a spot price vector. Define positivity, convexity, cones, and dual cones. State the no-arbitrage axioms using linear algebra and orthants. Deduce the Fundamental Theorem on Asset Pricing from Farkas's Lemma and also from convex cone self-double-duality. Define complete and incomplete markets using matrix models. Compute risk neutral probabilities for both invertible and noninvertible market matrices. Find no-arbitrage bid-ask intervals in an incomplete market using linear programming software.
