Tsallis Entropy for Loss Models and Survival Models Involving Truncated and Censored Random Variables.

The aim of this paper consists in developing an entropy-based approach to risk assessment for actuarial models involving truncated and censored random variables by using the Tsallis entropy measure. The effect of some partial insurance models, such as inflation, truncation and censoring from above and truncation and censoring from below upon the entropy of losses is investigated in this framework. Analytic expressions for the per-payment and per-loss entropies are obtained, and the relationship between these entropies are studied. The Tsallis entropy of losses of the right-truncated loss random variable corresponding to the per-loss risk model with a deductible d and a policy limit u is computed for the exponential, Weibull, χ2 or Gamma distribution. In this context, the properties of the resulting entropies, such as the residual loss entropy and the past loss entropy, are studied as a result of using a deductible and a policy limit, respectively. Relationships between these entropy measures are derived, and the combined effect of a deductible and a policy limit is also analyzed. By investigating residual and past entropies for survival models, the entropies of losses corresponding to the proportional hazard and proportional reversed hazard models are derived. The Tsallis entropy approach for actuarial models involving truncated and censored random variables is new and more realistic, since it allows a greater degree of flexibility and improves the modeling accuracy.

Volatility Dynamics of Non-Linear Volatile Time Series and Analysis of Information Flow: Evidence from Cryptocurrency Data.

This paper aims to empirically examine long memory and bi-directional information flow between estimated volatilities of highly volatile time series datasets of five cryptocurrencies. We propose the employment of Garman and Klass (GK), Parkinson's, Rogers and Satchell (RS), and Garman and Klass-Yang and Zhang (GK-YZ), and Open-High-Low-Close (OHLC) volatility estimators to estimate cryptocurrencies' volatilities. The study applies methods such as mutual information, transfer entropy (TE), effective transfer entropy (ETE), and Rényi transfer entropy (RTE) to quantify the information flow between estimated volatilities. Additionally, Hurst exponent computations examine the existence of long memory in log returns and OHLC volatilities based on simple R/S, corrected R/S, empirical, corrected empirical, and theoretical methods. Our results confirm the long-run dependence and non-linear behavior of all cryptocurrency's log returns and volatilities. In our analysis, TE and ETE estimates are statistically significant for all OHLC estimates. We report the highest information flow from BTC to LTC volatility (RS). Similarly, BNB and XRP share the most prominent information flow between volatilities estimated by GK, Parkinson's, and GK-YZ. The study presents the practicable addition of OHLC volatility estimators for quantifying the information flow and provides an additional choice to compare with other volatility estimators, such as stochastic volatility models.

Evaluation of the quality of lentic ecosystems in Romania by a GIS based WRASTIC model.

Globally, ecosystems are constantly degrading as a result of pressures derived from human activities and climate change. For working towards the restoration of the natural balance, it is necessary to evaluate the deviations induced in the ecosystems, to identify where the changes took place, to know what is their amplitude and to decide where it is possible to get involved. Many aquatic ecosystems are depreciated and their restoration is often difficult. Development of appropriate assessment methodologies will improve the decision-making process in public policies for environmental protection and conservation of biodiversity. This study presents an assessment of the degradation level of lentic ecosystems in Romania, performed through a multi-criteria analysis. An extension of the WRASTIC index (Wastewater-Recreational-Agricultural-Size-Transportations-Indutrial-Cover) was generated, namely WRASTIC-HI. The new index was obtained by including values derived from the Potential Pollutant Load index. The analysis showed that 13% of the evaluated lakes are natural, 56.5% are semi-degraded and 30.5% are degraded. The proposed methodology allows to determine the spatial distribution of the degradation sources and to calculate the corresponding indicators. The results obtained provide a useful tool for diagnostic step that can be used as a cornerstone to further identification of environmental conflicts and proposals for improvement of the ecological status of the lentic ecosystems.