This laboratory has as its goal the use of mathematical tools in the study and solution of real world problems coming from the applied sciences. In particular, we have studied problems coming from biophysical and financial applications. In the biophysical sciences we can cite applications to image reconstruction & tomography, structured populations, and virus dynamics. In the financial applications we can mention the study of risk management, commodity modelling, volatility estimation, and project evaluation under uncertainty.

**"**Incomplete Markets**"**

Prof. Teemu Pennanen - King's College London

April, 03, 05, 10 e 12, 2018 - Room 232, from 5:30 to 7:00 pm

Abstract: This is a set of 4 lectures so as to give an introduction to asset-liability management, accounting and indifference pricing in terms of basic optimization theory. Our aim is to give a unified treatment of the above concepts and to study their relations and basic properties with minimal mathematical sophistication. Mathematical techniques are introduced only when they become necessary for the development of the theory. Working with discrete-time models allows us to avoid many of the technicalities associated with continuous time models. This leaves room for practical considerations that are sometimes neglected in more mathematiWorking with discrete-time models allows us to avoid many of the technicalities associated with continuous time models. This leaves room for practical considerations that are sometimes neglected in more mathematical texts. In particular, we extend the classical theory of mathematical finance by allowing for nonlinear illiquidity effects and portfolio constraints.

Such features are significant in practice but they invalidate much of the classical theory. We deviate from the classical theory also in that we do not insist on the existence of a perfectly liquid numeraire asset. This means that one can no longer postpone payments by shorting the numeraire so the payment schedule of a financial contract becomes an important issue. This is essential in practice where much of trading consists of exchanging sequences of cash-flows. Examples include loans as well as various swap and insurance contracts where both claims and premiums involve payments at several points in time.cal texts. In particular, we extend the classical theory of mathematical finance by allowing for nonlinear illiquidity effects and portfolio constraints.Such features are significant in practice but they invalidate much of the classical theory. We deviate from the classical theory also in that we do not insist on the existence of a perfectly liquid numeraire asset. This means that one can no longer postpone payments by shorting the numeraire so the payment schedule of a financial contract becomes an important issue. This is essential in practice where much of trading consists of exchanging sequences of cash-flows. Examples include loans as well as various swap and insurance contracts where both claims and premiums involve payments at several points in time.

Minicourse by Prof. Nicolas Vauchelet on *PDE Models Applied to Biology*

*This is a short course where the audience will be introduced to important models in Biology that can be described by partial differential equations(PDEs).
Among these models we emphasize drift-diffusion equations for invading species, which has an important application in the case of trying to control dengue mosquitos by means of the Wolbachia bacteria. Another example concerns structured population equations. The area is quite rich of relevant applications and challenging problems. The level of the course will be adjusted according to the audience but in principle one expects a certain familiarity with basic concepts of Analysis and PDEs such as the Fourier transform, Sobolev spaces and the heat equation.*

For more information click here.

Research in Options RiO 2018 started with an impressive array of leading scientists and market practitioners.

For more info click here.

General audience paper on the importance of mathematical algorithms in present day life published in Portuguese. Click here to download the paper.

We are happy and proud to announce the first part of the Special Issue of the International Journal of Theoretical and Applied Finance about the meetings Research in Options that were organized in IMPA during the period 2006 till 2017.

The first issue includes papers of several well-known names in the field of Quantitative Finance. For more information click on the image bellow:

We are happy to inform you that the paper "Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model" is now published online in Vol. 15, no. 4 August 2018 regular issue in Mathematical Biosciences & Engineering. In this article the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)?

The article can be found here.

It is our pleasure to announce the release of the book **“New Trends in
Parameter Identification for Mathematical Models”** in the series "Trends in Mathematics". by Bernd Hofmann, Antonio Leitão, and Jorge P.

Zubelli. For more information see:

LAMCA's advisory board member and collaborator, Benoît Perthame has been elected to the French Academy of Sciences. See here.

LAMCA's collaborator Wenceslao González Manteiga has been elected to the Galician Academy of Sciences. See here.

We are happy to announce the success of the events:

See:

- Article in the newspaper
*O Estado de São Paulo*about Bruno Dupire and the event Research in Options. - Article about Mathematical Modeling of Criminal Behavior.
- Article about the Mathematics of the World Cup Draw.

Upcoming text "New Trends in Parameter Identification for Mathematical Models" edited by B. Hofmann, A. Leitão and J.P. Zubelli announced by Springer.

INVERSE PROBLEMS AT WORK!!! The importance of Inverse Problems in the Applied Sciences is once more confirmed by the Nobel prize award to Prof. Joachim Frank" of Columbia University for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution" jointly with Jacques Dubochet and Richard Henderson.

The methodology behind such technique involves the solution of a difficult inverse problem and has been the subject of intense investigation by many groups. It is in the cross roads of many research areas including numerical analysis, computer science and optimization.

We at LAMCA have been actively working in inverse problems and in 2003 published jointly with the group of Prof. Gabor T. Herman the article

"Three-dimensional reconstruction by Chahine's method from electron microscopic projections corrupted by instrumental aberrations" in the journal Inverse Problems where we studied the issue of high-resolution imaging for cryo-microscopy and proposed a class of algorithms based on a classical method of Chahine's.

LAMCA participates at the CEMRACS 2017 at the CIRM in Luminy, France.

See Talk: "Project Evaluation under Uncertainty" by J.P. Zubelli

**Paper published in Physical Review B:**

"Theory and measurements of harmonic generation in semiconductor superlattices with applications in the 100 GHz to 1 THz range"

by M. F. Pereira, J. P. Zubelli, D. Winge, et al.

**Manuscript accepted in the SIAM** **Journal on Numerical Analysis:**

"A non-intrusive stratified resampler for regression Monte Carlo:

application to solving non-linear equations"

by E. Gobet, G. Liu, and J.P. Zubelli

**Paper published (online first)
Data driven recovery of local volatility surfaces **

on

by V. Albani, U. Ascher, Xu. Yang, and J.P. Zubelli.

Discussion group on the Statistical PlanAb for the OTIM-PBR project.

March 13-15, 2017

Project Evaluation under Uncertainty: The Hedged Monte Carlo Approach.

Jorge P. Zubelli - IMPA

24/04/2017, 19:00 - room 232

Abstract : Industrial strategic decisions have evolved tremendously in the last decades towards a higher degree of quantitative analysis. Such decisions require taking into account a large number of uncertain variables and volatile scenarios, much like financial market investments. Furthermore, they can be evaluated by comparing to portfolios of investments in financial assets such as in stocks, derivatives and commodity futures. This revolution led to the development of a new field of managerial science known as Real Options. The use of Real Option techniques incorporates also the value of flexibility and gives a broader view of many business decisions that brings in techniques from quantitative finance and risk management. Such techniques are now part of the decision making process of many corporations and require a substantial amount of mathematical background. Yet, there has been substantial debate concerning the use of risk neutral pricing and hedging arguments to the context of project evaluation. We discuss some alternatives to risk neutral pricing that could be suitable to evaluation of projects in a realistic context with special attention to projects dependent on commodities and non-hedgeable uncertainties. More precisely, we make use of a variant of the hedged Monte-Carlo method of Potters, Bouchaud and Sestovic to tackle strategic decisions. This is joint work with E.Brigatti (UFRJ), F.Macias (BTG Chile) and M.O.Souza (UFF).