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No-Arbitrage Principle in Conic Finance

Department of Mathematics, Western Michigan University, 1903 West Michigan Avenue, Kalamazoo, MI 49008, USA
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Risks 2020, 8(2), 66; https://doi.org/10.3390/risks8020066
Received: 1 May 2020 / Revised: 8 June 2020 / Accepted: 9 June 2020 / Published: 19 June 2020
(This article belongs to the Special Issue Portfolio Optimization, Risk and Factor Analysis)
In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in 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 the bid–ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a 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. View Full-Text
Keywords: conic finance; convex optimization; arbitrage pricing conic finance; convex optimization; arbitrage pricing
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Vazifedan, M.; Zhu, Q.J. No-Arbitrage Principle in Conic Finance. Risks 2020, 8, 66.

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