We present an arbitrage free theoretical framework for modeling nonlinear bid and ask prices of dividend paying securities in a discrete time setup using the theory of dynamic acceptability indices. We develop the theory of dynamic sub-scale invariant performance measures and provide a representation of such measures in terms of g-expectations, and solutions of BSDeltaE with convex drivers. Then, we discuss a market model for dividend paying securities by introducing the pricing operators that are defined in terms of dynamic acceptability indices. Using these pricing operators, we define the bid and ask prices for the underlying securities and derivatives in the market. We show that the obtained market model is arbitrage free and a series of properties of these prices.

This is a joint work with Tomasz R. Bielecki and Igor Cialenco.