We propose a method for obtaining the maximum likelihood estimators of the parameters of the Markov-Modulated Diffusion Risk Model in which the inter-claim times, the claim sizes, and the volatility diffusion process are influenced by an underlying Markov jump process. We consider cases when this process has been observed in two scenarios: first, only observing the inter-claim times and the claim sizes in an interval time, and second, considering the number of claims and the underlying Markov jump process at discrete times. In both cases, the data can be viewed as incomplete observations of a model with a tractable likelihood function, so we propose to use algorithms based on stochastic Expectation-Maximization algorithms to do the statistical inference. For the second scenario, we present a simulation study to estimate the ruin probability. Moreover, we apply the Markov-Modulated Diffusion Risk Model to fit a real dataset of motor insurance.

我们提出了一种获得马尔可夫调制扩散风险模型参数的最大似然估计量的方法，其中索赔间时间、索赔规模和波动率扩散过程受到潜在马尔可夫跳跃过程的影响。我们考虑在两种情况下观察到此过程的情况：首先，仅观察间隔时间内的索赔间时间和索赔大小，其次，考虑离散时间的索赔数量和潜在的马尔可夫跳跃过程。在这两种情况下，数据都可以被视为具有易处理似然函数的模型的不完整观察，因此我们建议使用基于随机期望最大化算法的算法来进行统计推断。对于第二种情况，我们提出了一项模拟研究来估计破产概率。