Chuancun Yin

We study the optimal investment and per-loss reinsurance problem for an insurer in a financial market with stochastic factors, where claim arrivals are governed by a dynamic contagion process. The claim intensity incorporates exogenous shocks, endogenous self-excitation, and stochastic fluctuations, thereby capturing the clustering behavior of insurance claims.

Abstract Stochastic orders provide a powerful method for comparing random variables based on their distributions, extensively studied by many scholars. However, in reality, it is often difficult to obtain the true distribution of a random variable due to data limitations. To address this challenge, we introduce a novel concept of robust stochastic order, where the distribution of the random variable is estimated within a family of distributions.

Abstract This paper introduces range moment (RM), range skewness (RS), and kurtosis (RK). We derive the formula of RM for the univariate elliptical family, with emphasis on normal, student-t, logistic, Laplace, and Pearson type VII distributions. We also present explicit expressions of the range Value-at-Risk (RVaR), variance (RV), RS, and RK for those distributions. Moreover, the RVaR for sum of elliptical risks is derived.