# Mathematical Challenges

###### Mathematical Challenge January 2019

Some properties of collision operators in kinetic theory

Download PDF###### Mathematical Challenge November 2018

Autoencoder-based collaborative filtering algorithms

Download PDF###### Mathematical Challenge March 2018

Abstractive, multi-document, query-related text summarization

Download PDF###### Mathematical Challenge December 2017

Artificial intelligence is nowadays a buzzword and various distortions of its original meaning are common. Indeed, even the original and technical meaning is not univocal. AI may refer to the development of artificial systems showing either human like or rational behavior. Furthermore, it can be distinguished between systems that try to achieve this via either human-like or not human-like internal structures.

Download PDF###### Mathematical Challenge October 2017

Both Solvency II and the Swiss Solvency Test require insurance companies to model the one-year P&L distribution of their asset-liability portfolio. The solvency capital is then determined as either the 99.5% VaR (Solvency II) or the 99% CVaR (Swiss Solvency Test) of this distribution.

Download PDF###### Mathematical Challenge September 2017

Bayesian networks are graphical models, which represent multivariate probability distributions [1]. Nodes correspond to variables and directed edges represent the probability factorization

Download PDF###### Mathematical Challenge August 2017

Large scale optimization problems arise often due to a large number of optimization variables or, as in machine learning tasks, due to a large number of training data to fit the model on. Distributed optimization algorithms, where computations are performed in parallel relying only on local observations and information, are appealing to reduce computational time and sometimes, in case of lack of a centralized access to information for example, unavoidable.

Download PDF###### Mathematical Challenge July 2017

The efficient-market hypothesis developed by Fama states that asset prices fully reflect all available information. Therefore, according to the theory, no one can consistently outperform the market by using the same information that is already available to all investors.

Yet, a wide range of pricing anomalies are observed, suggesting that profitable portfolio strategies can be formulated [1]. Among the many candidates for the greatest anomaly, a particularly compelling one is the long-term success of low-volatility and low-beta portfolios...

###### Mathematical Challenge June 2017

Many mathematical procedures allow to find exposure coefficients (called betas [1]) of a financial

instrument respectively to a selection of risk factors. Whereas most of these techniques provide

point-estimate betas, the Bayesian Model Averaging (BMA) framework allows to compute beta

distributions. We first briefly describe the formulas and procedure underneath these distributions.

We then state the driven portfolio optimization problem.

###### Mathematical Challenge May 2017

Model boosting is a very successful and widely used technique to build classifiers [1]. Essentially, it allows to obtain a powerful ensemble classifier from a “weak” base classifier, whose error rate is slightly better than random guessing.

Download PDF###### Mathematical Challenge March 2017

In this mathematical challenge we present the Entropy Pooling approach, introduced by A. Meucci as a generalization of the Black-Litterman approach.

Download PDF###### Mathematical Challenge February 2017

In this challenge, we succinctly present old as well as new considerations about Recurrent Neural Networks, and the main practical challenges when fitting them.

Download PDF###### Mathematical Challenge January 2017

Chaos is a property of some dynamical systems that is generally loosely defined as “sensitivity to initial conditions”.

Download PDF###### Mathematical Challenge April 2013

In today’s digital environment, proper transmission of data is crucial, however most of the transmissions are sent through noisy channels. For example, consider a CD player reading from a scratched music CD, or a wireless cell phone capturing a weak signal from a relay tower which is too far away. These situations give rise to problems in communication which must be solved if one is to transmit information reliably. For the following discussion, let us assume that all the messages are sent through a memoryless binary symmetric channel.

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