In the research of the natural ecological environment, environmental scattering is an important research content whose results are widely used. In order to fully study the relevant characteristics of the natural grassland environment, this paper established a grassland broadband clutter model, summarized the dominant and recessive laws of the grassland environment broadband clutter, and provided a new perspective for related environmental monitoring which would be helpful to solve the problem of target detection in complex environments. The main work of this paper is as follows: The dielectric constant model of the grass was established, and the curve of the dielectric constant with frequency was obtained. The Monte Carlo method combined with the Gaussian spectrum function was used to generate a two-dimensional Gaussian surface to simulate the actual grass surface. A broadband clutter model was established, and, considering the calculation efficiency and accuracy, the Sparse Matrix/Canonical Grid (SMCG) was used to calculate the surface scattering coefficient. Then, the environmental clutter amplitude with different radar bandwidth (10, 40, 80 MHz), surface roughness (h = 0.1 m, h = 0.2 m, h = 0.4 m) and grazing angle (30°, 60°) were calculated and the probability density function (PDF) was obtained. The results show that the higher the radar resolution, the larger the incident angle, and the rougher the interface, all of which will cause the tail of the PDF to become longer which will not only reduce the detection probability of the radar, but also the tracking accuracy. The research results can be used for civilian and military field.

In non-life insurance, business sustainability requires accurate and robust predictions of reserves related to unpaid claims. To this aim, two different approaches have historically been developed: aggregated loss triangles and individual claim reserving. The former has reached operational great success in the past decades, whereas the use of the latter still remains limited. Through two illustrative examples and introducing an appropriate tree-based algorithm, we show that individual claim reserving can be really promising, especially in the context of long-term risks.

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

In this paper, we provide a novel approach to studying the heavy-tailed asymptotics of the stationary probability vector of a Markov chain of GI/G/1 type, whose transition matrix is constructed from two matrix sequences referred to as a boundary matrix sequence and a repeating matrix sequence, respectively. We first provide a necessary and sufficient condition under which the stationary probability vector is heavy tailed. Then we derive the long-tailed asymptotics of the R-measure in terms of the RG-factorization of the repeating matrix sequence, and a Wiener-Hopf equation for the boundary matrix sequence. Based on this, we are able to provide a detailed analysis of the subexponential asymptotics of the stationary probability vector.