Minerva Foundation Lectures
This page is an archive. See the current page for the Minerva Lectures here.
These special lecture series in probability and mathematical finance
are made possible by the generous support of the Minerva
Research Foundation. Time and location vary.
Spring Semester 2016
March 21 — March 23
Fall Semester 2015
September 28 — October 2
October 13—22
November 2 — November 11
Spring Semester 2015

March 911
 Title
Integrable Combinatorics
 Abstract
Integrability occurs in physical problems with sufficiently many
symmetries, and allows for exact, often elegant solutions with deep
geometric and algebraic meaning. Such problems often boil down to that
of enumerating weighted configurations of particular systems, which can
be rephrased in purely combinatorial or probabilistic terms.
In these lectures, we review manifestations of integrability in various
enumeration problems such as Lorentzian Triangulations, Planar Maps,
Alternating Sign Matrices, Domino Tilings, Plane Partitions, Current
Algebra Tensor Product Multiplicities, and their interplay with the
underlying structure of Cluster Algebra and its quantum deformation.
 Time and location:
Monday March 9, 5:307:00pm, 507 Math [w/ the Informal MathPhysics seminar]
Tuesday March 10, 5:307:00pm, 622 Math
Wednesday March 11, 4:106pm, 417 Math (tbc)
 Slides: Lecture 1; Lecture 3.
Spring Semester 2014

Mon Apr 21 and Thu Apr 24, 5:307pm, Math 507
Macdonald processes
Abstract:
Our goal is to explain how certain basic representation theoretic ideas
and constructions encapsulated in the form of Macdonald processes lead
to nontrivial asymptotic results in various `integrable' probabilistic
problems. Examples include dimer models, general beta random matrix
ensembles, and various members of the (2+1)d anisotropic KPZ and
(1+1)d KPZ universality classes, such as growing stepped surfaces,
qTASEP, qPushASEP, and directed polymers in random media.

Fri Apr 25, 11am12noon, School of Social Work 903
Gaussian Free Field in beta ensembles and random surfaces
Abstract:
The goal of the talk is to argue that the
twodimensional Gaussian Free Field is a universal and unifying object
for global fluctuations of spectra of random matrices and random
surfaces. This viewpoint leads to natural Gaussian processes on larger
spaces which, despite their explicit covariance structure, so far lack
conceptual understanding.
Also note the propaedeutic talk:

Mon Apr 14, 5:307pm, Math 507  Informal Mathematical Physics seminar
Macdonald polynomials for everyone
Fall Semester 2013
Spring Semester 2012
Fall Semester 2011

September 715, 2011
 Denis Talay
(INRIA, SophiaAntipolis)
Model Risk: Modeling, Analysis, Control and Numerics
Poster
All lectures are 90 minutes.
Lecture I: 9 am September 7 in Room 903 SSW
Lecture II: 9 am September 8 in Room 507 Math
Lecture III: 9 am September 12 in Room 903 SSW
Lecture IV: 9 am September 14 in Room 903 SSW
Lecture V: 9 am September 15 in Room 507 Math
Abstract for lectures:
The objective of these lessons is to show that model risk analysis,
particularly financial model risk analysis, opens new interesting
stochastic analysis problems, to present recent mathematical and
numerical techniques to tackle them, and to analyze mathematically
some robust strategies which, issued from the technical analysis, do
not rely on a specific mathematical model. We will also present a
selection of challeng ing open questions.
Various theories will be used, such as statistics of random processes,
stochastic control, Malliavin calculus, backward stochastic
differential equations, viscosity solutions of nonlinear Partial
Differential equations. However the course will be selfcontained
and, whenever possible, the proofs will be fully detailed.

September 22October 27, 2011
 Vladas Sidoravicius
(IMPA)
Phase transitions in stochastic processes with longrange interactions:
a multiscale analysis approach
Poster
Thursdays 9:1010:40am in Mathematics Hall 507.
Abstract:
Stochastic processes with longrange interactions play an important role
in many areas of science, ranging from abstract questions of Probability
Theory and Statistical Mechanics to applied problems in biology,
genetics, chemistry and many others.
During my lectures I will focus on three classical onedimensional models:
longrange percolation, Ising model and Markov chains with complete
connections. Processes with longrange interaction even in one dimensional
case present very rich and complex behavior, and undergo phase transitions.
However due to infinite range of interactions the behavior of systems is
very complex and traditional techniques fail to capture the picture. One
of aims of this course is to introduce and explain some very powerful
multiscale analysis techniques (with their roots in Renormalization Group
approach), which are remarkably efficient in the present situation.
The course will follow nearly chronologically the development of a
beautiful chapter of modern Probability (and Statistical Mechanics), which
started with W. Doeblin, and I will explain fundamental works of Freeman
Dyson, J. Frohlich and T. Spencer, C. Newman and L. Schulman, M. Bramson
and S. Kalikow, whose deep ideas shaped this field.
During the course I will also explain all necessary techniques and basic
concepts from Percolation Theory and Random Spatial Processes. The course
requires knowledge of basic Probability and Markov Chains.
Spring Semester 2011

February 18, 2011
 Johannes MuhleKarbe
(ETH Zurich)
Shadow
Prices in Portfolio Optimization with Transaction
Costs
Poster
Lecture I: 46 pm February 1 in Room 312 Math
Lecture II: 46 pm February 3 in
Room 312 Math
Lecture III: 46 pm February 7 in Room 622 Math
Lecture IV: 46 pm February 8 in Room 312 Math.
Abstract for lectures:
Talk I, Feb 1: Motivation, History, and Existence (based on
http://arxiv.org/abs/0911.4801 and some new results, joint work with Jan
Kallsen, Mark Owen, and Luciano Campi)
Abstract: A ``shadow price'' is a process evolving within the bidask spread
of a market with proportional transaction cots, such that the maximal
expected utility in this frictionless market is the same as in the original
market with transaction costs. In this talk, we introduce this concept and
also outline its origins, which go back to Jouini & Kallal (J. Econom.
Theory, 1995), Kusuoka (Annals Appl. Probab., 1995), and Cvitanic & Karatzas
(Math. Finance, 1996). We also present an elementary existence proof for
finite probability spaces. Moreover, we discuss work in progress on
existence in more general setups.
Talk II, Feb 3: The GrowthOptimal Portfolio under Transaction Costs (based on
http://arxiv.org/abs/1005.5105, joint work with Stefan Gerhold and Walter
Schachermayer)
Abstract: In this talk, we discuss how to use the idea of ``shadow prices''
for computations. More specifically, we determine a shadow price whose
growthoptimal portfolio coincides with the one for proportional transaction
costs in the BlackScholes model. This provides a new simple proof for the
results of Taksar et al. (Math. Oper. Res., 1988). Moreover, it also leads
to asymptotic expansions of the optimal policy and the maximal growth rate
for small transaction costs.
Talk III, Feb 7: Maximizing LogUtility from Consumption under Transaction Costs
(based on http://arxiv.org/abs/1010.4989 resp.
http://arxiv.org/abs/1010.0627, joint work with Jan Kallsen resp. Stefan
Gerhold and Walter Schachermayer)
Abstract: We revisit the problem of maximizing expected logarithmic utility
from consumption over an infinite horizon in the BlackScholes model with
proportional transaction costs, as studied in the seminal paper of Davis and
Norman (Math. Oper. Res., 1990). As in Talk II, we tackle this problem by
determining a shadow price. Moreover, for small transaction costs, we again
determine power series of arbitrary order for the optimal policy and the
value function. This extends work of Janecek and Shreve (Finance Stoch.,
2004), who determined the firstorder terms.
Talk IV, Feb 8: LongRun Optimal Portfolios under Transaction Costs (work in
progress, joint with Stefan Gerhold, Paolo Guasoni, and Walter
Schachermayer)
Abstract: The computations in Talks II and III crucially exploited that the
investor's preferences are modeled by a logarithmic utility function. In
this talk, we describe how to determine shadow prices also for power utility
functions. More specifically, we focus on the longrun optimal portfolio in
the BlackScholes model with proportional transaction costs and provide a
rigorous proof for the results of Dumas and Luciano (J. Finance, 1991).
Moreover, we again explain how to obtain full asymptotic expansions for the
optimal policy and the optimal growth rate.

March 29April 1, 2011
 Darrell Duffie
(Stanford University)
Dark Markets
Poster
Tuesday, March 29
10:30am  12:00pm, SSW 1025
Wednesday, March 30
10:30am  12:00pm, SSW 1025
Friday, April 1
12:00pm  1:00pm, SSW 903
Abstract for lectures:
The financial crisis of 20072009 brought significant concerns and
regulatory action regarding the role of overthecounter markets,
particularly from the viewpoint of financial instability. Overthe
counter markets for derivatives, collateralized debt obligations, and
repurchase agreements played particularly important roles in the cri
sis and in subsequent legislation in U.S. and Europe. This legisla
tion has also focused on increasing competition and transparency. The
modeling of OTC markets, however, is still relatively undeveloped in
comparison to the available research on central market mechanisms.
Rather than trading through a centralized mechanism such as an
auction, specialist, or limitorder book, overthecounter mar ket
participants negotiate terms privately with other market partici
pants, often pairwise. Overthecounter investors may be largely
un aware of prices that are currently available elsewhere in the
market, or of recent transactions prices. In this sense, OTC markets
are relatively opaque; investors are somewhat in the dark about the
most attractive available terms and about who might offer
them. These lectures addresses how prices, asset allocations, and
information transmission in OTC markets are influenced by this form
of opaque ness. The objective is to provide a brief introduction to
OTC mar kets, including some of the key conceptual issues and
modeling tech niques, and to provide a foundation for reading more
advanced re search in this topic area. The lectures assume a
graduatelevel background in probability theory.
Fall Semester 2010

December 320, 2010
 Boris L. Rozovsky
(Brown University)
Generalized Malliavin Calculus and Stochastic PDEs
Abstract for lectures: [pdf]
 Friday Dec 3, 121 pm in Math 520: Probability Seminar.
 Friday, Dec 3, 2.303.20 pm in Stat 1025: Lecture I. ``Stochastic Quantization and NavierStokes Equation.''
 Friday, Dec 10, 1011:30 am in Math 622: Lecture II. ``Introduction to Malliavin calculus''.
 Friday, Dec 17, 2.304.00 pm in Stat 1025: Lecture III. ``Generalized Malliavin calculus''.
 Monday, Dec 20, 1011.30 am in Stat 1025: Lecture IV. ``Bilinear stochastic PDEs driven by stationary noise''.

SPRING Semester 2010

April 1222, 2010
 Ofer Zeitouni (UMN & Weizmann Institute)
Random Walks in Random Environments

Mar 2529, 2010
 Geoffrey Grimmett (Cambridge)
Lattice models in probability

Mar 2225, 2010
 Walter Schachermeyer (Vienna)
The asymptotic theory of transaction costs


FALL Semester 2009
September 930, 2009
 Jean Bertoin (Universite Paris VI)
Exchangeable Coalescents



Spring Semester 2009


FebruaryApril, 2009

Hans Follmer (Berlin)
Convex Risk measures and their dynamics

January 2027, 2009

Sara Biagini (Pisa)
Topics in Portfolio Optimization


OctoberNovember, 2008
 Shige Peng (Sandong University)
Coherent and convex risk measures and nonlinear expectations