Nonlinear reserving and multiple contract modifications in life insurance

Marcus C. Christiansen; Boualem Djehiche

doi:10.1016/j.insmatheco.2020.05.004

Nonlinear reserving and multiple contract modifications in life insurance

Marcus C. Christiansen, Boualem Djehiche

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.

Original language	English (US)
Pages (from-to)	187-195
Number of pages	9
Journal	Insurance: Mathematics and Economics
Volume	93
DOIs	https://doi.org/10.1016/j.insmatheco.2020.05.004
State	Published - Jul 2020

Keywords

Backward SDEs
Implicit options
Nonlinear semi-Markov chain
Prospective reserve
Thiele equation

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

Access to Document

10.1016/j.insmatheco.2020.05.004

Cite this

@article{e0e1f8c3b89f4aaa9b92b47ef6048a45,

title = "Nonlinear reserving and multiple contract modifications in life insurance",

abstract = "Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.",

keywords = "Backward SDEs, Implicit options, Nonlinear semi-Markov chain, Prospective reserve, Thiele equation",

author = "Christiansen, {Marcus C.} and Boualem Djehiche",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = jul,

doi = "10.1016/j.insmatheco.2020.05.004",

language = "English (US)",

volume = "93",

pages = "187--195",

journal = "Insurance: Mathematics and Economics",

issn = "0167-6687",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Nonlinear reserving and multiple contract modifications in life insurance

AU - Christiansen, Marcus C.

AU - Djehiche, Boualem

PY - 2020/7

Y1 - 2020/7

N2 - Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.

AB - Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.

KW - Backward SDEs

KW - Implicit options

KW - Nonlinear semi-Markov chain

KW - Prospective reserve

KW - Thiele equation

UR - http://www.scopus.com/inward/record.url?scp=85085006760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85085006760&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2020.05.004

DO - 10.1016/j.insmatheco.2020.05.004

M3 - Article

AN - SCOPUS:85085006760

SN - 0167-6687

VL - 93

SP - 187

EP - 195

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

ER -

Nonlinear reserving and multiple contract modifications in life insurance

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this