In the article, we analyse the problem of the efficiency market hypothesis using entropy in moments of transition from a normal economic situation to crises or slowdowns in European, Asian and US stock markets and the economy in the years 2007–2023 (2008–2009, U.S. financial sector crises; 2020–2021, Pandemic period; and the 2022–2023 period of Russia’s attack on Ukraine). The following hypothesis is put forward in the article: In periods of economic slowdown and economic crises, the entropy of prices and return rates decreases. According to the principles of physics, in an isolated system, entropy increases and decreases at the moment of external intervention, similar to finance, where during crises and economic slowdowns, there is interference from governments introducing new regulations and intervening in financial markets. The article uses the Shannon entropy method. This measure, as a statistical measure, does not require the assumption of stationarity of time series or a known probability distribution, unlike classical statistical methods. Our results confirm decreased entropy in stock markets during crisis.

Companies that manage mandatory pension funds are frequently accused of excessive fee taking. International analyses have found that in countries with legal caps, commissions remain within these caps; hence, market competition does not function. Surprisingly, there are few international cases where local regulators implement mechanisms to facilitate competition. The variety of auction mechanisms available raises the question of whether an optimal solution exists for this purpose. Therefore, in this study, we present evidence, based on a controlled regulatory experiment, on the fee-reduction potential of reverse auctions.

In the recent decade, there has been observed across the Central and Eastern European states the regulatory trend towards the increase of the non-financial (first) pension pillar size at the expense of the financial (second) pillar. It tends to question the consequences of this shift for the future retirement benefits. Applying the portfolio approach we address this issue by running a series of simulations to find out how to allocate pension contributions between both pillars in an optimal way. Our study contributes to the existing literature as follows. First, we do not perform the assessment of the predetermined regulatory solutions, but we look for an optimal one. Moreover, we allow our optimal rule to be time-varying, if necessary, which would be a true novelty in this research area. Second, we do not base our estimates on historical trends; rather, we apply the long-term economy’s projection to account for the society’s ageing impact, which is a crucially important factor for the solvency of the pension system. Adapting some of the simulation assumptions to fit the Polish case, our results confirm that current regulations underestimate the role of the capital pillar and the optimal allocation between both pillars should be time-varying.

The paper analyzes the problem of entropy in the moments of transition from a normal economic situation (2015–2019) to the Pandemic period (2020–2021) and the period of Russia’s attack on Ukraine (2022–2023). The research in the article is based on the analysis of electricity, oil, coal, and gas prices in 27 countries of the European Union and Norway. The daily data cover the period from January 1, 2015, to March 30, 2023, and were analyzed using two-dimensional sets of electricity and commodity prices. The work uses the time dependent James-Stein estimator of the Shannon informational entropy.

The regulatory framework of the Polish pension system is far-removed from the optimal lifecycle portfolio approach, which recommends a time-varying asset mix to minimize portfolio risk. Nevertheless, a question emerges on how large diversification gains can grow under the existing rules. This study accounts for the current restrictions and estimates risk-reduction opportunities under the two-pillar pension system. We compare the outcomes with our previous results for optimal portfolio allocation and, as in the previous study, use a Monte Carlo approach with a copula function to simulate the distribution of replacement rates for the Polish pension system. We conclude that the regulations hinder, to a significant extent, the opportunity to minimize shortfall risks, an unsatisfactory outcome for Polish pensioners.