No-Arbitrage Principle in Conic Finance

Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Qiji Jim Zhu

Second Advisor

Dr. Yuri Ledyaev

Third Advisor

Dr. Jay Treiman

Fourth Advisor

Dr. Qing Zhang


The “No-Arbitrage" characterization has been long established in one price financial models as the Fundamental Theorem of Asset Pricing (FTAP). In one price economy, FTAP establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. In fact, such an equivalent measure can be derived as the unit normal vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in a two-price financial models (where there is a bid-ask price spread) the set of attainable gains is not a subspace anymore. We use convex optimization and the conic property of this region to characterize the No-Arbitrage principle in financial models with bid-ask price spread present. This characterization will lead us to the generation of a set of ordered pairs of martingale measures and discount random variables. Under such set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

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