‎‎‎Performance measures are essential for evaluating portfolio performance in the risk management and fund industries‎, ‎with the Sharpe ratio being a widely adopted risk-adjusted metric‎. ‎This ratio compares the excess expected return to its standard deviation‎, ‎enabling investors to assess the returns of risk-taking activities against risk-free options‎. ‎Its popularity stems from its ease of calculation and straightforward interpretation‎. ‎However‎, ‎the actual Sharpe ratio value is often unavailable and must be estimated empirically based on the assumption of normality of asset returns‎. ‎In practice‎, ‎financial assets typically exhibit non-normal distributions and nonlinear dependencies‎, ‎which can compromise the accuracy of the Sharpe ratio estimation when normality is assumed‎. ‎This paper challenges the normality assumption‎, ‎aiming to enhance the accuracy of Sharpe ratio estimates‎. ‎We investigate the impact of dependency on the Sharpe ratio of a two-asset portfolio using copulas‎. ‎Theoretical findings and extensive simulations demonstrate the effectiveness of the proposed copula-based approach to the classic Sharpe ratio‎.

‎‎‎Performance measures are essential for evaluating portfolio performance in the risk management and fund industries‎, ‎with the Sharpe ratio being a widely adopted risk-adjusted metric‎. ‎This ratio compares the excess expected return to its standard deviation‎, ‎enabling investors to assess the returns of risk-taking activities against risk-free options‎. ‎Its popularity stems from its ease of calculation and straightforward interpretation‎. ‎However‎, ‎the actual Sharpe ratio value is often unavailable and must be estimated empirically based on the assumption of normality of asset returns‎. ‎In practice‎, ‎financial assets typically exhibit non-normal distributions and nonlinear dependencies‎, ‎which can compromise the accuracy of the Sharpe ratio estimation when normality is assumed‎. ‎This paper challenges the normality assumption‎, ‎aiming to enhance the accuracy of Sharpe ratio estimates‎. ‎We investigate the impact of dependency on the Sharpe ratio of a two-asset portfolio using copulas‎. ‎Theoretical findings and extensive simulations demonstrate the effectiveness of the proposed copula-based approach to the classic Sharpe ratio‎.

Modeling dependence using copula functions is a standard and widely used method in applied statistics‎. ‎In recent years‎, ‎experiments have been conducted in which several dependent responses are described by regression models‎, ‎and then experimental designs for these models have been carried out‎. ‎These regression models are often expressed as copula-based regression models‎, ‎so the copula parameters (if they exist) also affect the optimal design problem‎. ‎In this paper‎, ‎we consider the dependence structure of a random pair from the exponential distribution conditionally upon a covariate as a regression model‎, ‎then investigate the D-optimal design for this copula-based regression model‎. ‎The copula function that is used is the Fréchet‎‎ copula‎. ‎The optimal designs obtained all have a general form depending on the selected design space.

The frequency and severity of extreme events have increased in recent years in many areas‎. ‎In the context of risk management for insurance companies‎, ‎reinsurance provides a safe‎ ‎solution as it offers coverage for large claims‎. ‎This paper investigates the impact of‎ ‎dependent extreme losses on ruin probabilities under four types of reinsurance‎: ‎excess of loss‎, ‎quota share‎, ‎largest claims‎, ‎and ecomor‎. ‎To achieve this‎, ‎we use the dynamic GARCH-extreme value theory-copula‎ ‎combined model to fit the specific features of claim data and provide more accurate estimates‎ ‎than classical models‎. ‎We derive the surplus processes and asymptotic ruin probabilities ‎under the Cramer-Lundberg risk process‎. ‎Using a numerical example with real-life data‎, ‎we illustrate the effects of dependence and the behavior of reinsurance strategies‎ ‎for both insurers and reinsurers‎. ‎This comparison includes risk premiums‎, ‎surplus processes‎, ‎risk measures‎, ‎and ruin probabilities‎. ‎The findings show that the GARCH-extreme value theory-copula model mitigates the over‎- ‎and under-estimation‎ ‎of risk associated with extremes and lowers the ruin probability for heavy-tailed distributions‎.