Using the language of convex analysis we describe key results in several important areas of finance: portfolio theory, financial derivative trading and pricing and consumption based asset pricing theory. We hope to emphasize the importance of convex analysis in financial mathematics and also bring attention to researchers in convex analysis interesting issues in financial applications.

Convexity has long had an important role in economic theory, but some recent developments have featured it all the more in problems of equilibrium. Here the tools of convex analysis are applied to a basic model of incomplete financial markets in which assets are traded and money can be lent or borrowed between the present and future. The existence of an equilibrium is established with technique...

In his ‘23’ “Mathematische Probleme” lecture to the Paris International Congress in 1900, David Hilbert wrote “Besides it is an error to believe that rigor in the proof is the enemy of simplicity.” In this spirit, we use simple convex analytic methods, relying on an ingenious function due to Simon Fitzpatrick, to provide a concise proof of the maximality of the sum of two maximal monotone opera...

The core is a central solution concept in cooperative game theory, and therefore it is important to know under what conditions the core of a game is guaranteed to be non-empty. Two notions that prove to be very useful in this context are Linear Programming (LP) duality and convexity. In this work, we apply these tools to identify games with overlapping coalitions (OCF games) that admit stable o...