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

A numerical study on the evolution of portfolio rules

In this paper we test computationally the performance of CAPM in an evolutionary setting. In particular we study the stability of distribution of wealth in a financial market where some traders invest as prescribed by CAPM and others behave according to different portfolio rules. Our study is motivated by recent analytical results that show that, whenever a logarithmic utility maximiser enters the market, CAPM traders vanish in the long run. Our analysis provides further insights and extends these results. We simulate a sequence of trades in a financial market and: first, we address the issue of how long is the long run in different parametric settings; second, we study the effect of heterogeneous savings behaviour on asymptotic wealth shares. We find that CAPM is particularly “unfit” for highly risky environments

The RTU Graduate School Executive Master's Program for school year 2011-2012 as viewed by its respondents

This study was conducted to ascertain the views and opinions of the faculty and personnel as recipients of the Rizal Technological University (RTU) Graduate School Executive Master's program as to its reasons for availment, importance of the core and major subjects of the curriculum, lecturers' professional skills, duration/time allotment, level of satisfaction, significant difference of the two programs, problem encountered and gathered possible solutions to the problems; determine whether the Executive Master's Program was able to realize its goals and objectives and find out the overall impression of the recipients about the Executive Master's Program. A total of fifty (50) RTU faculty and personnel graduated from this Executive Master's program, twenty six (26) Master of Arts in Education (MAEd) and twenty four (24) Master of Arts in Engineering (MAE)

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.

Nonparametric Entropy Estimation for Stationary Processes and Random Fields, with Applications to English Text

We discuss a family of estimators for the entropy rate of a stationary ergodic process and prove their pointwise and mean consistency under a Doeblin-type mixing condition. The estimators are Ces`aro averages of longest match-lengths, and their consistency follows from a generalized ergodic theorem due to Maker. We provide examples of their performance on English text, and we generalize our results to countable alphabet processes and to random fields. Index Terms -- Entropy rate, pattern matching, universal data compression, entropy of English. 1 I. Kontoyiannis and P. Algoet are with the Information Systems Laboratory (Durand 141A), Electrical Engineering Department, Stanford University, Stanford CA 94305. Email: [email protected], and [email protected]. Yu.M. Suhov is with the Statistical Laboratory, DPMMS, Cambridge University, and also with the Institute for Problems in Information Transmission, Moscow. Email: [email protected]. A.J. Wyner is with the Stat..

Temporal Profile and Limb-specificity of Phasic Pain-Evoked Changes in Motor Excitability

A fundamental function of nociception is to trigger defensive motor responses to threatening events. Here, we explored the effects of phasic pain on the motor excitability of ipsilateral and contralateral arms. We reasoned that the occurrence of a short-lasting nociceptive stimulus should result in a specific modulation of motor excitability for muscles involved in the withdrawal of the stimulated limb. This was assessed using transcranial magnetic stimulation (TMS) of the left and right primary motor cortex to elicit motor-evoked potentials (MEPs) in three flexor and two extensor muscles of both arms. To assess the time-course of nociception-motor interactions, TMS pulses were triggered 50–2000 ms after delivering short-lasting nociceptive laser stimuli to the left or right hand. We made three main observations. First, nociceptive stimuli induced an early-latency (100 ms) enhancement of MEPs in flexor muscles of the stimulated hand. Considering its latency, this modulation is likely consequent to nociceptive-motor interactions at spinal level. This early and lateralized enhancement was followed by a later (150–400 ms) MEP reduction in extensor muscles of the stimulated hand and flexor muscles of both hands, predominant at the stimulated hand. Finally, we observed a long-lasting (600–2000 ms) MEP enhancement in muscles of the non-stimulated hand. These later effects of the nociceptive stimulus could reflect nociception-motor interactions occurring at cortical level

Identification of Reality in Bayesian Context

Complexity has many facets as does any general concept. The relationship between "infinitely" complex reality and restricted complexity of the artificial world of models is addressed. Particularly, the paper tries to clarify the meaning of Bayesian identification under mismodelling by answering the question, "What is the outcome of the Bayesian identification without supposing the model set considered contains the "true" system model?" The answer relates known asympotic results to the "natural" finite-time domain of Bayesian paradigm. It serves as an interpretation "smoother" of those Bayesian identification results that quietly ignore the mismodelling present. Keywords: decision-making, model selection, Bayesian identification, approximation 1 Introduction System identification can be understood as the set of procedures which model an investigated part of reality (called object, process, plant or system) using data measured on it [8]. Modelling of the reality, often informal, is a n..