Stochastic forecasting and risk valuation are now front burners in a list of applied and theoretical sciences. In this work, we propose an unconventional tool for stochastic prediction of future expenses based on the individual (micro) developments of recorded events. Considering a firm, enterprise, institution, or any entity, which possesses knowledge about particular historical events, there might be a whole series of several related subevents: payments or losses spread over time. This all leads to an infinitely stochastic process at the end. The aim, therefore, lies in predicting future subevent flows coming from already reported, occurred but not reported, and yet not occurred events. The emerging forecasting methodology involves marked time-varying Hawkes process with marks being other time-varying Hawkes processes. The estimated parameters of the model are proved to be consistent and asymptotically normal under simple and easily verifiable assumptions. The empirical properties are investigated through a simulation study. In the practical part of our exploration, we elaborate a specific actuarial application for micro claims reserving.

随机预测和风险评估现在已成为应用科学和理论科学领域的佼佼者。在这项工作中，我们提出了一种非常规工具，用于根据记录事件的个人（微观）发展情况来随机预测未来的支出。考虑到拥有特定历史事件知识的公司，企业，机构或任何实体，可能会有一系列相关的子事件，包括一系列随时间变化的付款或损失。这最终导致了无限的随机过程。因此，目标在于预测来自已报告，已发生但未报告但尚未发生的事件的未来子事件流。新兴的预测方法涉及标记的时变霍克斯过程，而标记是其他时变的霍克斯过程。在简单且易于验证的假设下，该模型的估计参数被证明是一致且渐近正态的。通过模拟研究来研究经验性质。在我们探索的实践部分中，我们将详细介绍微要求保留的特定精算应用。