MathFinance Colloquium: Nonlinear Black Scholes Equations in Finance

We study properties of solutions to fully nonlinear versions of the standard Black-Scholes partial differential equation. These equations have been introduced in financial mathematics in order to deal with illiquid markets or with stochastic volatility. We show that typical nonlinear Black-Scholes equations can be viewed as dynamic programming equation of an associated control problem. We establish existence and comparison results and show that the equation induces a convex risk measure on the set of all continuous terminal value claims. Moreover, we study the asymptotic behavior of solutions as market frictions get `large'. Finally the pricing of individual contracts relative to a book of derivatives is discussed.

Lecture Room: Commerzbank