Extension of as-if-Markov modeling to scaled payments
提出将as-if-Markov建模方法扩展到多状态人寿保险中的按比例支付场景，通过测度变换简化计算，并给出估计方法，对精算师和保险建模者有用。
In multi-state life insurance, as-if-Markov modeling has recently been suggested as an alternative to Markov modeling in case of deterministic sojourn and transition payments. Incidental policyholder behavior, on the other hand, gives rise to duration-dependent payments in the form of so-called scaled payments. The goal of this paper is to establish as-if-Markov modeling also for scaled payments. To this end, we employ change of measure techniques to transfer the added complexity from the payments to an auxiliary probabilistic model. Based hereon, we show how to compute the accumulated cash flow by solving a system of equations comparable to Kolmogorov's forward equations for Markov chains, but with the transition rates replaced by certain forward transition rates related to the auxiliary probabilistic model. Finally, we provide feasible landmark estimators for these auxiliary forward transition rates subject to entirely random right-censoring.