Dependent interest and transition rates in life insurance

Buchardt, Kristian

doi:10.1016/j.insmatheco.2014.01.004

Cited by 17 publications

(19 citation statements)

References 10 publications

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“…Forward transition and interest rates in the context of dependency between markets risks and biometric and behavioral risks are therefore not discussed in this paper. To our knowledge, only Buchardt [2] has provided a forward rate concept allowing for successful replacement arguments in multi-state models with dependency between interest and transition rates. Buchardt [2] only considers simple models consisting of at most one non-absorbing state.…”

Section: Discussionmentioning

confidence: 99%

“…To our knowledge, only Buchardt [2] has provided a forward rate concept allowing for successful replacement arguments in multi-state models with dependency between interest and transition rates. Buchardt [2] only considers simple models consisting of at most one non-absorbing state. A natural next step is to extend the definition of forward equations rates and the definition of state-wise forward transition rates to allow for dependency between market risks and biometric and behavioral risks and compare the concepts to that of Buchardt [2].…”

Section: Discussionmentioning

confidence: 99%

“…Buchardt [2] only considers simple models consisting of at most one non-absorbing state. A natural next step is to extend the definition of forward equations rates and the definition of state-wise forward transition rates to allow for dependency between market risks and biometric and behavioral risks and compare the concepts to that of Buchardt [2].…”

Section: Discussionmentioning

confidence: 99%

“…Also, from (A.1) and [20] Theorem 3.4.1, Proof of Theorem 3. 2 We first show that there exists a unique solution to (3.5) for any T ∈ (t, ∞). Fix T ∈ (t, ∞).…”

Section: Discussionmentioning

confidence: 99%

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Forward transition rates

Buchardt¹,

Furrer

Steffensen

2019

Finance Stoch

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The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework for the discussion of forward rates. Furthermore, we provide a novel definition with its own logic and merits and compare it with the proposals in the literature. The definition turns the Kolmogorov forward equations inside out by interchanging the transition probabilities with the transition intensities as the object to be calculated.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Also, from (A.1) and [20] Theorem 3.4.1, Proof of Theorem 3. 2 We first show that there exists a unique solution to (3.5) for any T ∈ (t, ∞). Fix T ∈ (t, ∞).…”

Section: Discussionmentioning

confidence: 99%

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Forward transition rates

Buchardt¹,

Furrer

Steffensen

2019

Finance Stoch

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“…For an introduction to policyholder modeling and a comparison of various approaches, see [6] and the references therein. Attempts to couple the two approaches have been made for surrender behavior, where surrender occurs randomly, but where the probability is somewhat controlled by rational factors, e.g., [7,8]. From a Solvency 2 point of view, the modeling of policyholder behavior is required; see Section 3.5 in [9].…”

Section: Introductionmentioning

confidence: 99%

Life Insurance Cash Flows with Policyholder Behavior

Buchardt

Møller

2015

Risks

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The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation of simple integrals. In the second part, a more general disability model with recovery is studied. Here, cash flows are determined by solving a modified Kolmogorov forward differential equation. We conclude the paper with numerical examples illustrating the methods proposed and the impact of policyholder behavior.

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Chapter VII: Special Studies in Life Insurance

Asmussen

Steffensen

2020

Risk and Insurance

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Dependent interest and transition rates in life insurance

Cited by 17 publications

References 10 publications

Forward transition rates

Forward transition rates

Life Insurance Cash Flows with Policyholder Behavior

Chapter VII: Special Studies in Life Insurance

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