In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on independent errors with mean zero, which are stochastically dominated by the random variable epsilon and H-r(x)=E|epsilon|(R) I(|epsilon|<= x) is the slowly varying function at infinity. The weak consistencies for the estimators are established under infinite r-th(1 < r < 2 ) moments and other suitable conditions. The results obtained in the paper improve and generalize the existing ones of identically distributed random errors to the case of stochastically dominated random errors and the existing results under finite moments to the case of infinite moments. In addition, some simulation studies including numerical simulation and real data analysis are presented.
This paper investigates the second-order asymptotic tail behavior of stochastic discounted aggregate losses in a discrete-time model, capturing the multidimensional dependence between insurance and financial risks via a multivariate Farlie-Gumbel-Morgenstern distribution. Moving beyond the restrictive assumption of independence or bivariate dependence prevalent in the literature, we derive a second-order asymptotic approximation for the tail probability under the general condition that insurance risks possess a second-order subexponential tail. Our main result provides a closed-form expression that explicitly quantifies the impact of inter-risk dependencies, significantly refining the conventional first-order asymptotics. Simulation studies confirm that the proposed second-order formula markedly enhances estimation accuracy, offering a more reliable tool for capital allocation and risk management.
In this paper we study the potential measures and the Laplace transforms of the occupation times of a refracted-reflected spectrally negative Lévy process when the process is observed at the arrival epochs of two independent Poisson processes. In this case, the rates of observing the underlying process differ in time which deviates from the classical theory of Poissonian observations. Explicit expressions for the so-called Poissonian potential measures and the Poissonian occupation times are derived in terms of (known) scale functions. Other fluctuation identities are also derived.
