Speakers for Specialized Courses

by Peter Carr, Courant Institute of Mathematical Sciences (NYU) and Morgan Stanley

Monetary utility functions and capital requirements

by Kay Giesecke, Stanford University

Arbitrage-Free Pricing, Optimal Investment and Equilibrium

by Dmitry Kramkov, Carnegie Mellon University

Lévy and Sato processes calibrated and applied to problems of capital allocation and risk management using the theories of conic finance and nonlinear expectations

by Dilip Madan, University of Maryland at College Park

Optimal stochastic control and Backward SDEs

by Nizar Touzi, Ecole Polytechnique

COURSE DETAILS

Speaker: Peter Carr

Title: FX Options: challenges and opportunites

The theory originally developed by Black Scholes and Mertonfor pricing stock options was soon applied to FX options. We indicate the challenges that arise in an FX context where barrier options are also liquid. We review the classic theory of dynamic hedging in this context with application to vanillas, barrier options, and quantoed products. We also develop the theory of static hedging using vanilla and/or barrier options as hedge instruments. (↑)

Lecture notes: L1 L2 L3 L4

Speaker: Freddy Delbaen

Title: Monetary utility functions and capital requirements

I will present a summary of the theory of monetary utility functions. One of the applications is the calculation and allocation of the capital in financial institutions. First I will concentrate on the representation of such utility functions or risk measures. Then I will present some examples and will address the capital allocation problem. The last part will be devoted to time consistent utility functions which in continuous time will lead to Backward Stochastic Differential Equations. (↑)

Speaker: Kay Giesecke

Title: Credit risk with point processes

This short course will give an introduction to the modeling of credit risk and the valuation of credit derivatives from the perspective of point processes. It develops the required background in point processes, including transform analysis, Monte Carlo simulation, and statistical estimation. The course covers single name and portfolio credit risk, and treats corporate bonds, credit swaps, index contracts, and tranches of collateralized debt obligations. Examples involving real data are given. (↑)

Lecture notes

Speaker: Dilip B. Madan

Title: Lévy and Sato processes calibrated and applied to problems of capital allocation and risk management using the theories of conic finance and nonlinear expectations

The lectures will introduce Lévy and Sato Processes as models for option surfaces followed by a study of modeling dependence using Lévy processes. This will be followed by an introduction to Conic finance and two price economies with applications to identifying capital requirements, determining the value of the taxpayer put option and introducing the new hedging criterion of capital minimization. The procedures will be illustrated in both static and dynamic hedging contexts. (↑)

Lecture notes: L1 L2 L3 L4 L5 L6 L7

Speaker: Nizar Touzi

Title: Optimal stochastic control and Backward SDEs

We start with the classical theory of stochastic control and we show the benefit from viscosity solutions in order to derive the dynamic programming equation. We then provide the main ideas for the stochastic target problems where viscosity solutions is a key-tool. Finally, we provide the connection with Backward SDEs. Applications in finance will be provided throughout the lectures. (↑)

Lecture Notes

Speaker: Dmitry Kramkov

Title:Arbitrage-Free Pricing, Optimal Investment and Equilibrium

1) Tentative title and outline of your short five hour course.

Monetary Utility Functions and Capital Requirements

Lecture Notes