本项目将针对风险理论中若干问题的阶段观测建模、数值计算和非参数估计展开研究。首先，我们将研究阶段观测下风险模型中的分红、缴税问题，讨论风险测度、分红（缴税）总额的期望现值等的计算方法。其次，我们针对考虑投资的马尔科夫可加风险模型和高维风险模型展开研究，给出风险测度的数值计算方法。同时，我们还将考虑有限时间内的破产和分红问题，研究有限时间内风险测度和分红总额期望现值的数值计算方法。最后，在考虑投资的复合泊松风险模型和Levy风险模型下，我们研究破产概率和期望折现罚函数的统计估计方法，讨论估计量在大样本下的相合性、渐近正态性，并通过模拟验证有限样本下估计量的有效性。

In this project, we will study the periodic observation modeling, numerical computation and statistical estimation for some problems in risk theory. First, we study the dividend and tax strategies in risk models under periodic observation, and discuss how to compute the risk measures and the total expected discounted dividends (tax). Next, for the Markov additive risk model with investment and high dimension risk models, we develop numerical methods for computing the risk measures. Meanwhile, we will also consider the finite time horizon ruin and dividend problems, investigate the numerical methods for computing the finite time risk measures and the expected discounted dividend payments. Finally, for the compound Poisson risk model with investment and the Levy risk model, we study how to estimate the ruin probability and the expected discounted penalty function by statistical methods, study the consistency and asymptotic normality of the estimates under large sample setting, and verify the efficiency under finite sample size setting.