Applied Mathematics

Multisector matching with cognitive and social skills: a stylized model for education, work and marriage

Speaker: 
Robert McCann
Date: 
Tue, Sep 25, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Lecture Series
Abstract: 

Economists are interested in studying who matches with whom (and why) in the educational, labour, and marriage sectors. With Aloysius Siow, Xianwen Shi, and Ronald Wolthoff, we propose a toy model for this process, which is based on the assumption that production in any sector requires completion of two complementary tasks. Individuals are assumed to have both social and cognitive skills, which can be modified through education, and which determine what they choose to specialize in and with whom they choose to partner.

Our model predicts variable, endogenous, many-to-one matching. Given a fixed initial distribution of characteristics, the steady state equilibrium of this model is the solution to an (infinite dimensional) linear program, for which we develop a duality theory which exhibits a phase transition depending on the number of students who can be mentored. If this number is two or more, then a continuous distributions of skills leads to formation of a pyramid in the education market with a few gurus having unbounded wage gradients. One preprint is on the arXiv; a sequel is in progress.

Class: 

Optimal transportation with capacity constraints

Speaker: 
Robert McCann
Date: 
Wed, Aug 22, 2012 to Thu, Aug 23, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Lecture Series
Abstract: 

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a given cost function. Here we consider a variation of this problem by imposing an upper bound constraining the joint measures, namely: among all joint measures with fixed marginals and dominated by a fixed measure, find the optimal one. After computing illustrative examples, we given conditions guaranteeing uniqueness of the optimizer and initiate a study of its properties. Based on a preprint arXived with Jonathan Korman.

Class: 

Optimal Investment for an Insurance Company

Speaker: 
Alexandru Badescu
Location: 
Calgary Place Tower (Shell)
University of Calgary, Calgary, Canada
Conference: 
Shell Lunchbox Lectures
Abstract: 

Optimal investment is a key problem in asset-liability management of an insurance company. Rather than allocating wealth optimally so as to maximize the overall investment return, an insurance company is interested in assessing the risk exposure where both assets and liabilities are included and minimizing the risk of mismatches between them. Different approaches for solving optimization problems by minimizing standard risk measures such as the value at risk (VaR) or the conditional value at risk (CVaR) have been proposed in the literature. In this paper we focus on some Solvency II applications by investigating several novel problems for jointly quantifying the optimal initial capital requirement and the optimal portfolio investment under various constraints.

Discussions on the convexity of these problems are also provided. Using a Monte Carlo simulation and a semi-parametric approach based on different assumptions for the loss distribution, we compute the insurer optimal capital needed to be efficiently invested in a portfolio formed by two or more assets. Finally, a detailed numerical experiment is conducted to assess the robustness and sensitivity of our optimal solutions relative to the model factors.

This paper was written in collaboration with Alexandru V. Asimit (Cass Business School, City University, UK), Tak Kuen Siu (Faculty of Business and Economics, Macquarie University, Australia)and Yuriy Zinchenko (Department of Mathematics and Statistics, University of Calgary).

Class: 

Hugh C. Morris Lecture: George Papanicolaou

Speaker: 
George Papanicolaou
Date: 
Tue, Nov 8, 2011
Location: 
PIMS, University of British Columbia
Conference: 
Hugh C. Morris Lecture
Abstract: 

N.B. The audio introduction of this lecture has not been properly captured.

The quantification of uncertainty in large-scale scientific and engineering computations is rapidly emerging as a research area that poses some very challenging fundamental problems which go well beyond sensitivity analysis and associated small fluctuation theories. We want to understand complex systems that operate in regimes where small changes in parameters can lead to very different solutions. How are these regimes characterized? Can the small probabilities of large (possibly catastrophic) changes be calculated? These questions lead us into systemic risk analysis, that is, the calculation of probabilities that a large number of components in a complex, interconnected system will fail simultaneously.

I will give a brief overview of these problems and then discuss in some detail two model problems. One is a mean field model of interacting diffusion and the other a large deviation problem for conservation laws. The first is motivated by financial systems and the second by problems in combustion, but they are considerably simplified so as to carry out a mathematical analysis. The results do, however, give us insight into how to design numerical methods where detailed analysis is impossible.

Class: 

Brains and Frogs: Structured Population Models

Speaker: 
Kerry Landman
Date: 
Sat, Jul 16, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
2011 IGTC Summit
Abstract: 

In diverse contexts, populations of cells and animals disperse and invade a spatial region over time. Frequently, the individuals that make up the population undergo a transition from a motile to an immotile state. A steady-state spatial distribution evolves as all the individuals settle. Moreover, there may be multiple releases of motile subpopulation. If so, the interactions between motile and immotile subpopulations may affect the final spatial distribution of the various releases. The development of the brain cortex and the translocation of threatened Maud Island frog are two applications we have considered.

Class: 

Patterns of Social Foraging

Speaker: 
Leah Keshet
Date: 
Fri, Jul 15, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
2011 IGTC Summit
Abstract: 

I will present recent results from my group that pertain to spatio-temporal patterns formed by social foragers. Starting from work on chemotaxis by Lee A. Segel (who was my PhD thesis supervisor), I will discuss why simple taxis of foragers and randomly moving prey cannot lead to spontaneous emergence of patchiness. I will then show how a population of foragers with two types of behaviours can do so. I will discuss conditions under which one or another of these behaviours leads to a winning strategy in the sense of greatest food intake. This problem was motivated by social foraging in eiderducks overwintering in the Belcher Islands, studied by Joel Heath. The project is joint with post-doctoral fellows, Nessy Tania, Ben Vanderlei, and Joel Heath.

Class: 

The Broughton Archipeligo Monitoring Program

Speaker: 
Stephanie Peacock
Date: 
Fri, Jul 15, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
2011 IGTC Summit
Abstract: 

This talk was one of the IGTC Student Presentations.

Class: 

Modeling Spotting in Wildland Fire

Speaker: 
Jonathan Martin
Date: 
Thu, Jul 14, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
2011 IGTC Summit
Abstract: 

This talk was one of the IGTC Student Presentations.

Class: 

Life History Variations and the Dynamics of Structured Populations

Speaker: 
Romain Richard
Date: 
Thu, Jul 14, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
2011 IGTC Summit
Abstract: 

This talk was one of the IGTC Student Presentations.

Class: 

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