Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

A Polynomial Optimization Approach to Constant Rebalanced Portfolio Selection

We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers.

SPS WANF Dismantling: A Large Scale-Decommissioning Project at CERN

The operation of the SPS (Super Proton Synchrotron) West Area Neutrino Facility (WANF) was halted in 1998. In 2010 a large scale-decommissioning of this facility was conducted. Besides CERN’s commitment to remove non-operational facilities, the additional motivation was the use of the installation (underground tunnels and available infrastructure) for the new HiRadMat facility, which is designed to study the impact of high-intensity pulsed beams on accelerator components and materials. The removal of 800 tons of radioactive equipment and the waste management according to the ALARA (As Low As Reasonably Achievable) principles were two major challenges. This paper describes the solutions implemented and the lessons learnt confirming that the decommissioning phase of a particle accelerator must be carefully studied as from the design stage