The growth-optimal portfolio optimization strategy pioneered by Kelly is based on constant portfolio rebalancing which makes it sensitive to transaction fees. We examine the effect of fees on an example of a risky asset with a binary return distribution and show that the fees may give rise to an...

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem,...

We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a probabilistic response of the system elements to stress...

A model of open economics composed of producers and speculators is investigated by numerical simulations. The capital flows from the environment to the producers and from them to the speculators. The price fluctuations are suppressed by the speculators. When the aggressivity of the speculators...

We study the role of active and passive investors in an investment market with uncertainties. Active investors concentrate on a single or a few stocks with a given probability of determining the quality of them. Passive investors spread their investment uniformly, resembling buying the market...

When assets are correlated, benefits of investment diversification are reduced. To measure the influence of correlations on investment performance, a new quantity - the effective portfolio size - is proposed and investigated in both artificial and real situations. We show that in most cases, the...

Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [Kelly (1956)] that...

We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random walk with identical drift and dispersion. The rules of...

We consider a simple market where a vendor offers multiple variants of a certain product and preferences of both the vendor and potential buyers are heterogeneous and possibly even antagonistic. Optimization of the joint benefit of the vendor and the buyers turns the toy market into a...

We present and study a Minority Game based model of a financial market where adaptive agents -- the speculators -- interact with deterministic agents -- called producers. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of...