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

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..