A Markov-switching generalized additive model for compound Poisson processes, with applications to operational loss models
提出一种结合泊松和广义帕累托分布的马尔可夫切换广义加性复合过程模型，用于描述操作损失的时变依赖结构，并基于意大利银行欺诈数据验证了其在估计尾部风险指标上的优越性。
This paper is concerned with modelling the behaviour of random sums over time. Such models are particularly useful to describe the dynamics of operational losses, and to correctly estimate tail-related risk indicators. However, time-varying dependence structures make it a difficult task. To tackle these issues, we formulate a new Markov-switching generalized additive compound process combining Poisson and generalized Pareto distributions. This flexible model takes into account two important features: on the one hand, we allow all parameters of the compound loss distribution to depend on economic covariates in a flexible way. On the other hand, we allow this dependence to vary over time, via a hidden state process. A simulation study indicates that, even in the case of a short time series, this model is easily and well estimated with a standard maximum likelihood procedure. Relying on this approach, we analyse a novel data-set of 819 losses resulting from frauds at the Italian bank UniCredit. We show that our model improves the estimation of the total loss distribution over time, compared to standard alternatives. In particular, this model provides estimations of the 99.9% quantile that are never exceeded by the historical total losses, a feature particularly desirable for banking regulators.