Extension of as-if-Markov modeling to scaled payments

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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Extension of as-if-Markov modeling to scaled payments. / Christiansen, Marcus C.; Furrer, Christian.

In: Insurance: Mathematics and Economics, Vol. 107, 2022, p. 288-306.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Christiansen, MC & Furrer, C 2022, 'Extension of as-if-Markov modeling to scaled payments', Insurance: Mathematics and Economics, vol. 107, pp. 288-306. https://doi.org/10.1016/j.insmatheco.2022.09.001

APA

Christiansen, M. C., & Furrer, C. (2022). Extension of as-if-Markov modeling to scaled payments. Insurance: Mathematics and Economics, 107, 288-306. https://doi.org/10.1016/j.insmatheco.2022.09.001

Vancouver

Christiansen MC, Furrer C. Extension of as-if-Markov modeling to scaled payments. Insurance: Mathematics and Economics. 2022;107:288-306. https://doi.org/10.1016/j.insmatheco.2022.09.001

Author

Christiansen, Marcus C. ; Furrer, Christian. / Extension of as-if-Markov modeling to scaled payments. In: Insurance: Mathematics and Economics. 2022 ; Vol. 107. pp. 288-306.

Bibtex

@article{c4c2b23410c2454286cef9b7e911bcea,

title = "Extension of as-if-Markov modeling to scaled payments",

abstract = "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.",

keywords = "Incidental policyholder behavior, Kolmogorov's forward equations, Landmark estimators, Life insurance, Non-Markov models",

author = "Christiansen, {Marcus C.} and Christian Furrer",

note = "Publisher Copyright: {\textcopyright} 2022 The Author(s)",

year = "2022",

doi = "10.1016/j.insmatheco.2022.09.001",

language = "English",

volume = "107",

pages = "288--306",

journal = "Insurance: Mathematics and Economics",

issn = "0167-6687",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Extension of as-if-Markov modeling to scaled payments

AU - Christiansen, Marcus C.

AU - Furrer, Christian

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