Probability distortions for constructing nonlinear G-expectations for the bid and ask or lower and upper prices in continuous time are here extended to the direct use of measure distortions. Fairly generally measure distortions can be constructed as probability distortions applied to an...

For longer horizons, assuming no dividend distributions, equilibrium models for discounted stock prices are formulated as conditional expectations of nontrivial terminal random variables defined at infinity. Observing that extant models fail to have this property, new models are proposed. The...

Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro-differential equations that are solved numerically for the three...

A positive spot rate model driven by a gamma process and correlated to equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple (r,y,s) is...

The logarithm of SPX is modeled as a Sato process running at a speed proportional to the current level of the VIX. When the logarithm of the VIX is an exponential compound Poisson process with drift one may obtain exact expressions for the prices of equity options taken at an independent...