March 15, 2020
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in particular, any risk neutral distribution can be interpreted as a certificate establishing that no arbitrage exists. We are interested in the case when there are multiple risk-neutral probabilities. We describe a number of convex optimization problems over the convex set of risk neutral price probabilities.