Extension of as-if-Markov modeling to scaled payments
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Extension of as-if-Markov modeling to scaled payments. / Christiansen, Marcus C.; Furrer, Christian.
I: Insurance: Mathematics and Economics, Bind 107, 2022, s. 288-306.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Extension of as-if-Markov modeling to scaled payments
AU - Christiansen, Marcus C.
AU - Furrer, Christian
N1 - Publisher Copyright: © 2022 The Author(s)
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Incidental policyholder behavior
KW - Kolmogorov's forward equations
KW - Landmark estimators
KW - Life insurance
KW - Non-Markov models
UR - http://www.scopus.com/inward/record.url?scp=85139190346&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2022.09.001
DO - 10.1016/j.insmatheco.2022.09.001
M3 - Journal article
AN - SCOPUS:85139190346
VL - 107
SP - 288
EP - 306
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -
ID: 322798927