# Mathematical Finance

### Overview

There is a significant research activity in Mathematical Economics in Western Canada. However, this research has no supporting network. Our goal is to promote interdisciplinary cooperations among Canadian experts in mathematics, finance, economics and econometrics, and to establish an internationally visible network of academic excellence in mathematical economics. To this end, we aim to organize a two-year concentration period on The Economics and Finance of Climate Risk and Natural Resources starting September 2006. This will include a variety of training and research opportunities for young mathematicians and economists. Our research and training activities will focus on:

- Hedging and Insurance of Climate and Energy Risk
- Mathematics of Economic Geography and Resource Management
- Contract Theory

As this includes the numerical analysis of equilibrium, Numerical Methods for Partial Differential Equations constitute the fourth focal point of our research.

The analysis of the economic and financial risks associated with climate change has become one of the most active and challenging fields of research for mathematicians and economists. However, a unified framework for managing and hedging these risks has not yet been established. Our research project is related to the management of those risks. We focus on three specific topics. The first (Hedging and insurance of climate and energy risk) deals with the issue of pricing and hedging of insurance contracts written on non-financial risk factors such as climate phenomena. In the second approach we question how a well established line of research in economic (economic geography) could help in addressing the issues of managing climate risks and natural resources. In the third approach (contract theory), we address the issue of how to design financial and insurance contracts (or securities) to enhance the risk sharing. We believe that these topics, and their interplay, do not only fit well into our own research agenda, but will also attract the interest of many other scientists at PIMS universities.

### PIMS Distinguished Chairs and Visitors

- Pierre-Andre Chiappori (Economics, Columbia University) UBC, May 8-14, 2006
- Jean-Charles Rochet (Institut d'Economie Industrielle, Universite de Toulouse) UBC, July 10-August 15, 2006, "Dynamic contract theory and corporate finance."
- R. T. Rockafellar (University of Washington) UBC, July 10-17 2006: "Duality and equilibrium."
- Ken Judd (Hoover Institution) UBC, July 10-17, 2006: "Computational methods in economics."
- Roger Guesnerie (College de France, Paris) UBC, April 23-29, 2007

### Faculty

*CRG Leaders*

- Ulrich Horst (UBC)
- Alejandro Jofre (CMM Chile)

*Faculty from PIMS member universities:*

- SFU - Michael Robson (Econ)
- UBC - Ivar Ekeland (Math and Econ), Stephane Mellet (Math), Anthony Peirce (Math), Mike Peters (Math), Maurice Queyranne (Business)
- UNBC - Ali Lazrak (Business)
- UVic - Martial Agueh (Math), Cornelius van Kooten (Econ)

*Faculty from other institution members:*

- Felipe Alvarez (CMM)
- Raul Manasevich (CMM)