Applied Mathematics

Contingent Capital and Financial Networks 1

Speaker: 
Paul Glasserman
Date: 
Mon, Jul 21, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

These lectures will cover two topics. The first is contingent capital in the form of debt that converts to equity when a bank 
nears financial distress. These instruments offer a potential solution to the problem of banks that are too big to fail by 
providing a credible alternative to a government bail-out. Their properties are, however, complex. I will discuss models for the analysis of contingent capital with particular emphasis on their incentive effects and the design of the conversion trigger. The second topic in these lectures is the problem of quantifying contagion and amplification in financial networks. In particular, I will focus on bounding the potential impact of network effects under the realistic condition that detailed information on the structure of the network is unavailable

Diffusion Models for Systemic Risk 1

Speaker: 
Jean-Pierre Fouque
Date: 
Mon, Jul 21, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

We will present inter-bank borrowing and lending models based on systems of coupled diffusions. First-passage models will 
be reviewed and applied to mean-field type models in order to illustrate systemic events and compute their probability via 
large deviation theory. Then, a game feature will be introduced and Nash equilibria will be derived or approximated using the 
Mean Field Game approach.

Over the Counter Markets

Author: 
Darrell Duffie
Date: 
Thu, Jul 17, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

This lecture is part of a series on "Risk Sharing in Over-the-Counter Markets"

Financial System Architecture

Author: 
Darrell Duffie
Date: 
Wed, Jul 16, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

These lecture notes are part of a series on "Risk Sharing in Over-the-Counter Markets"

Oceans and Multiplicative Ergodic Theorems

Speaker: 
Anthony Quas
Date: 
Tue, Mar 25, 2014
Location: 
Calgary Place Tower (Shell)
Conference: 
Shell Lunchbox Lectures
Abstract: 

In many physical processes, one is interested in mixing and obstructions to mixing: warm air currents mixing with cold air; pollutant dispersal etc. Analogous questions arise in pure mathematics in dynamical systems and Markov chains. In this talk, I will describe the relationship between obstructions to mixing and eigenvectors of transition operators; in particular I will focus on recent work on the non-stationary case: when the Markov chain or dynamical system is non-homogeneous, or when the physical process is driven by external factors.

I will illustrate my talk with analysis of and data from ocean mixing.

Mathematics and the Planet Earth: a Long Life Together II

Speaker: 
Ivar Ekeland
Date: 
Wed, Jul 17, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Mathematics of Planet Earth 2013
Abstract: 

When Colombus left Spain in 1492, sailing West, he knew that the Earth was round and was expecting to land in Japan. Seventeen centuries earlier, around 200 BC, Eratosthenes had shown that its circumference was 40,000 km, just by a smart use of mathematics, without leaving his home town of Alexandria. Since then, we have learned much more about Earth: it is a planet, it has an inner structure, it carries life , and at every step mathematics have been a crucial tool of discovery and understanding. Nowadays, concerns about the human footprint and climate change force us to bring all this knowledge to bear on the global problems facing us. This is the last challenge for mathematics: can we control change?
This is a two-part lecture, investigating how our idea of the world has influenced the development of mathematics. In the first lecture on July 15, I will describe the situation up to the twentieth century, in the second one on July 17 I will follow up to the present time and the global challenges humanity and the planet are facing today.
 

Mathematics and the Planet Earth: a Long Life Together I

Speaker: 
Ivar Ekeland
Date: 
Mon, Jul 15, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Mathematics of Planet Earth 2013
Abstract: 
When Colombus left Spain in 1492, sailing West, he knew that the Earth was round and was expecting to land in Japan. Seventeen centuries earlier, around 200 BC, Eratosthenes had shown that its circumference was 40,000 km, just by a smart use of mathematics, without leaving his home town of Alexandria. Since then, we have learned much more about Earth: it is a planet, it has an inner structure, it carries life , and at every step mathematics have been a crucial tool of discovery and understanding. Nowadays, concerns about the human footprint and climate change force us to bring all this knowledge to bear on the global problems facing us. This is the last challenge for mathematics: can we control change?
This is a two-part lecture, investigating how our idea of the world has influenced the development of mathematics. In the first lecture (July 15), I will describe the situation up to the twentieth century, in the second one (July 17) I will follow up to the present time and the global challenges humanity and the planet are facing today.

Strong Oracle Optimality of Folded Concave Penalized Estimation

Speaker: 
Jianqing Fan
Date: 
Thu, May 23, 2013
Location: 
PIMS, University of British Columbia
Conference: 
International Workshop on the Perspectives on High Dimensional Data Analysis III
Abstract: 
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation.
However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimal solution computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution using the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely produces the same estimator in the next iteration. We show that the LASSO is a good initial estimator, which produces the oracle estimator using the one-step LLA algorithm for folded concave penalization methods. This is demonstrated by using three classical sparse estimation problems, namely, the sparse linear regression, the sparse logistic regression and the sparse precision matrix estimation, and illustrates the power of combining the LASSO and SCAD to solve sparse inartistical estimation problem.
(joint work with Lingzhou Xue and Hui Zou)

A Computational Mathematician Combusts

Speaker: 
Margot Gerritsen
Date: 
Fri, Jan 18, 2013
Location: 
PIMS, University of Calgary
Conference: 
Mathematics of Planet Earth 2013
Abstract: 
Large scale production of very heavy oil is gaining momentum because of the decline of easy to produce reservoirs, the increasing oil demand and subsequent rising oil price, which makes such resources more economical. Considering the pressure on the oil market and our still very heavy dependence on oil, this move to heavy oil production seems inevitable. Typically, heavy oil reservoirs are stimulated thermally. Injecting steam that is generated at the surface is not always viable or desirable. An alternative technique for production is In-Situ Combution (ISC) where a steam drive is generated in the reservoir itself. In this process, (enriched) air is injected in the reservoir. After ignition a combustion front develops in-situ that burns a small percentage of the oil in place and slowly moves through the reservoir producing steam along the way. A side benefit of this process is that the heat thus generated often cracks the oil into heavy, undesirable components (the "guck") that stay behind in the reservoir and lighter, more valuable components that can be brought up to the surface. Performance prediction of ISC projects is rather tricky and poses many computational challenges. In this talk I'll discuss our work in ISC simulation, which is centered around the design of upscaling methods for kinetics and critical reservoir heterogeneities supported by laboratory experimentation.
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