Markov chain modeling of policyholder behavior in life insurance and pension

Lars Frederik Brandt Henriksen; Jeppe Woetmann  Nielsen; Mogens Steffensen; Christian Svensson

doi:10.1007/s13385-014-0091-2

Markov chain modeling of policyholder behavior in life insurance and pension

Lars Frederik Brandt Henriksen, Jeppe Woetmann Nielsen, Mogens Steffensen, Christian Svensson

Department of Mathematical Sciences

7 Citations (Scopus)

Abstract

We calculate reserves regarding expected policyholder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modelling of insurance risk and behavioral risk in terms of free policy risk and surrender risk. We discuss valuation techniques in the cases where behavior is modeled to occur independently or dependently of insurance risk, respectively. Ordinary differential equations make it easier to work with dependence between insurance risk and behavior risk. We analyze the effects of the underlying behavioral assumptions for two contracts. For a “new” contract with low technical interest rate relative to the market interest rate, we obtain the lowest reserve by counting in dependence. For an “old” contract with high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and independence.

Original language	English
Journal	European Actuarial Journal
Volume	4
Issue number	1
Pages (from-to)	1-29
ISSN	2190-9733
DOIs	https://doi.org/10.1007/s13385-014-0091-2
Publication status	Published - 1 Jul 2014

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10.1007/s13385-014-0091-2

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title = "Markov chain modeling of policyholder behavior in life insurance and pension",

abstract = "We calculate reserves regarding expected policyholder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modelling of insurance risk and behavioral risk in terms of free policy risk and surrender risk. We discuss valuation techniques in the cases where behavior is modeled to occur independently or dependently of insurance risk, respectively. Ordinary differential equations make it easier to work with dependence between insurance risk and behavior risk. We analyze the effects of the underlying behavioral assumptions for two contracts. For a “new” contract with low technical interest rate relative to the market interest rate, we obtain the lowest reserve by counting in dependence. For an “old” contract with high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and independence.",

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AU - Nielsen, Jeppe Woetmann

AU - Steffensen, Mogens

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Y1 - 2014/7/1

N2 - We calculate reserves regarding expected policyholder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modelling of insurance risk and behavioral risk in terms of free policy risk and surrender risk. We discuss valuation techniques in the cases where behavior is modeled to occur independently or dependently of insurance risk, respectively. Ordinary differential equations make it easier to work with dependence between insurance risk and behavior risk. We analyze the effects of the underlying behavioral assumptions for two contracts. For a “new” contract with low technical interest rate relative to the market interest rate, we obtain the lowest reserve by counting in dependence. For an “old” contract with high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and independence.

AB - We calculate reserves regarding expected policyholder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modelling of insurance risk and behavioral risk in terms of free policy risk and surrender risk. We discuss valuation techniques in the cases where behavior is modeled to occur independently or dependently of insurance risk, respectively. Ordinary differential equations make it easier to work with dependence between insurance risk and behavior risk. We analyze the effects of the underlying behavioral assumptions for two contracts. For a “new” contract with low technical interest rate relative to the market interest rate, we obtain the lowest reserve by counting in dependence. For an “old” contract with high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and independence.

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