Scientific

Contingent Capital and FInancial Networks 2

Speaker: 
Paul Glasserman
Date: 
Wed, Jul 23, 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

Class: 
Scientific
Subject: 
Mathematics
Econometrics
Applied Mathematics

Financial Stability 3

Speaker: 
Jean-Charles Rochet
Date: 
Wed, Jul 23, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

The lender of last resort: An analysis of the economics and politics of banking crises, and episodes of bail-outs of
failing financial institutions.

  • Rochet Vives (2004) “The Lender of last Resort: was Bagehot right after all?” JEEA, 6, 1116-1147, reprinted in Rochet J.C. (2008) “Why are there so many banking crises?, Princeton University Press, chapter 2
Class: 
Scientific
Subject: 
Mathematics
Econometrics
Applied Mathematics

Risk Sharing in Over the Counter Markets 3

Speaker: 
Darrel Duffie
Date: 
Fri, Jul 25, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 
I will begin with an overview of the purpose and structure of OTC markets, and how they can be a source of systemic risk.
This will be followed by a brief review of search-based theories of trade and information sharing in OTC markets. Then I will turn to theories and evidence regarding the use of collateral, the role of central clearing, and failure management. The failure management topic will finish with a model of the efficient application of legal stays that could be imposed on OTC contracts at the point of bankruptcy or administrative failure resolution. These stays can yield effective payment or settlement priority to OTC contracts. Stays can be efficient, or not efficient, depending on the setting. The affected OTC contracts include derivatives, repurchase agreements, securities lending agreements, and clearing agreements. I assume a basic knowledge of game theory and of measure-theoretic probability theory, particularly counting processes with an intensity.
Class: 
Scientific
Subject: 
Mathematics
Econometrics
Applied Mathematics

Channels of Contagion in Financial Systems 3

Speaker: 
Rama Cont
Date: 
Fri, Jul 25, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

Understanding the mechanisms underlying systemic risk requires to change the traditional focus of risk modelling and examine the link between the structure of the financial system and its stability, with a focus on contagion mechanisms which may lead to large scale instabilities in the financial system. Some channels of contagion which have played an important role in past crises are: insolvency contagion through counterparty exposures, withdrawal of liquidity in funding channels and price-mediated contagion through fire sales of assets.

We review some recent work on the mechanisms underlying these channels of contagion, with a focus on the nature of the 'network' underlying each contagion mechanism and the implications of these results for the monitoring and regulation of systemic risk. In particular, we will attempt to illustrate the importance of the ineraction between these various channels and how this interaction may undermine regulatory efforts focussed only on a single mechanism.

Class: 
Scientific
Subject: 
Mathematics
Econometrics
Applied Mathematics

Channels of Contagion in Financial Systems 2

Speaker: 
Rama Cont
Date: 
Thu, Jul 24, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

Understanding the mechanisms underlying systemic risk requires to change the traditional focus of risk modelling and examine the link between the structure of the financial system and its stability, with a focus on contagion mechanisms which may lead to large scale instabilities in the financial system. Some channels of contagion which have played an important role in past crises are: insolvency contagion through counterparty exposures, withdrawal of liquidity in funding channels and price-mediated contagion through fire sales of assets.

We review some recent work on the mechanisms underlying these channels of contagion, with a focus on the nature of the 'network' underlying each contagion mechanism and the implications of these results for the monitoring and regulation of systemic risk. In particular, we will attempt to illustrate the importance of the ineraction between these various channels and how this interaction may undermine regulatory efforts focussed only on a single mechanism.

Class: 
Scientific
Subject: 
Econometrics
Applied Mathematics

Channels of Contagion in Financial Systems

Speaker: 
Rama Cont
Date: 
Thu, Jul 24, 2014
Location: 
PIMS, University of British Columbia
Conference: 
The Economics and Mathematics of Systemic Risk and Financial Networks
Abstract: 

Understanding the mechanisms underlying systemic risk requires to change the traditional focus of risk modelling and examine the link between the structure of the financial system and its stability, with a focus on contagion mechanisms which may lead to large scale instabilities in the financial system. Some channels of contagion which have played an important role in past crises are: insolvency contagion through counterparty exposures, withdrawal of liquidity in funding channels and price-mediated contagion through fire sales of assets.

We review some recent work on the mechanisms underlying these channels of contagion, with a focus on the nature of the 'network' underlying each contagion mechanism and the implications of these results for the monitoring and regulation of systemic risk. In particular, we will attempt to illustrate the importance of the ineraction between these various channels and how this interaction may undermine regulatory efforts focussed only on a single mechanism.

Class: 
Scientific
Subject: 
Mathematics
Econometrics
Applied Mathematics

Risk Sharing in Over the Counter Markets 2

Speaker: 
Darrel Duffie
Date: 
Wed, Jul 23, 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"

Class: 
Scientific
Subject: 
Mathematics
Econometrics
Applied Mathematics

Undecidability in Number Theory

Speaker: 
Bjorn Poonen
Date: 
Mon, May 26, 2014
Location: 
PIMS, University of British Columbia
Conference: 
2014 Niven Lecture
Abstract: 

Hilbert’s Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers.  Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists.  However, the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

Class: 
Scientific
Subject: 
Mathematics
Number Theory

High dimensional expanders and Ramanujan complexes

Speaker: 
Alexander Lubotzky
Date: 
Fri, Sep 19, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

Expander graphs have played, in the last few decades, an important role in computer science, and  in the last decade, also in pure mathematics.  In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam).  The talk will survey the various directions of research and their applications, as well as potential applications in math and CS.  Some of these lead to questions about buildings and representation theory of p-adic groups.

 

We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of  { S. Evra, K. Golubev,  T. Kaufman,  D. Kazhdan , R. Meshulam, S. Mozes }

Class: 
Scientific
Subject: 
Mathematics
Computer Science

The rank of elliptic curves

Speaker: 
Benedict Gross
Date: 
Fri, Oct 10, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

After quadratic equations in two variables come cubic equations, or elliptic curves. The set of rational points on an elliptic curve has the structure of a finitely generated abelian group. I will recall the basic theory of elliptic curves, then discuss the conjecture of Birch and Swinnerton-Dyer, which attempts to predict the rank of the group of rational points from the number of solutions (mod p) for all primes p. I will also discuss some recent results on the average rank, due to Manjul Bhargava and his collaborators. (PIMS-UBC Distinguished Colloquium)

Class: 
Scientific
Subject: 
Mathematics
Number Theory

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