No arbitrage for two price economies with no locally risk free asset implies that suitably deflated prices are nonlinear martingales. However, both the deflating process and the measure change depend on the process being deflated. Further assumptions allow the nonlinear martingales in discrete...

Learning the pre limited liability value process of equity claims and its relationship to the stock price is an answer to the financial jeorpardy question when observed option prices are the answer being given by the market. Constant dollar equity holder values, prior to the imposition of...

Prices in financial markets must move continuously and surprisingly to support their levels with returns. Consequently the function announcing the arrival rate of moves of different sizes becomes the equilibrium object, necessitating a reformulation of risk reward concepts in these terms. It is...

Markets passively accept a convex cone of cash flows that contains the the nonnegative cash flows. Different markets are defined by different cones and conditions are established to exclude the possibility of arbitrage between markets. Operationally these cones are defined by positive...

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and...

Two new indices for financial diversity are proposed. The first is aggregative and evaluates distance from a single factor driving returns. The second evaluates how fast correlation with a stock rises as the stock falls. Both measures are here risk neutral. The CRI is also compared with coVaR....