utility function

With the aim of portfolio optimization and management, this article utilizes the Clayton-copula along with copula theory measures. Portfolio-Optimization is one of the activities in investment funds. Thus, it is essential to select an appropriate optimization method. In modern financial analyses, there is growing evidence indicating the distribution of proceeds of financial properties is not customary. However, in common risk management methods the main assumption is that the distribution of assets returns is normal. When the distribution of earnings isn’t normal, the linear correlation coefficient isn’t considered to be an appropriate measure to express the dependency structure. The investors are required to make use of methods that concentrate on the aggregated risks, considering the whole positions and the links between risk factors and assets. Therefore, we use copula as an alternative measure to model the dependency structure in this research. In this regard, given the weekly data pertaining to the early 2002 until the late 2013, we use Clayton-copula to generate an optimized portfolio for both copper and gold. Finally, the Sharpe ratio obtained through this method is compared with the one obtained through Markowitz mean-variance analysis to ascertain that Clayton-copula is more efficient in portfolio-optimization.

Objective : This study aims to develop and apply two advanced social welfare functions that enhance sensitivity to income inequality and risk aversion, focusing on improving the welfare of lower-income groups in the context of income tax policy design. Methods : The study critiques classical social welfare models—such as utilitarian and aggregative approaches—for their limited responsiveness to inequality and social behaviors. It introduces two alternative frameworks: i) A function based on the Atkinson inequality index, capturing societal aversion to income disparities. ii) A function utilizing constant relative risk aversion (CRRA) utility, modeling individual welfare under income volatility. These models evaluate the effects of varying income tax rates on overall social welfare, accounting for average income and its distribution across societal strata. Results : The analysis shows that increasing income tax rates across all income groups reduces social welfare due to lower post-tax incomes, even when redistribution is intended. Individuals with higher levels of risk aversion experience greater welfare losses, emphasizing the importance of incorporating inequality sensitivity and risk aversion into policy design. Conclusion : The proposed social welfare functions offer more robust analytical tools for optimizing income tax policies. They promote equitable income distribution and improved social welfare by integrating distributive justice and risk-averse behavior. These models provide practical guidance for policymakers balancing economic efficiency with social justice.