Kolmogorov’s forward PIDE and forward transition rates in life insurance

Buchardt, Kristian

doi:10.1080/03461238.2016.1160255

Cited by 6 publications

(11 citation statements)

References 15 publications

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“…Because the forward equations rates are defined directly from (3.2), the above discussion shows that any general definition of forward transition rates that is to satisfy both (3.2) and (3.3) cannot be F µ t -measurable (and thus must be allowed to depend on the current state X t ). This motivates the forward transition rate definition of Buchardt [4] which we discuss in the following section.…”

Section: Proof See Appendix Amentioning

confidence: 92%

“…Another part of our contribution is the establishment of a theoretical framework for the discussion and comparison of forward rate definitions. This allows us to give a clear presentation of the relation between the different suggestions pushed forward by Christiansen and Niemeyer [6], Buchardt [4], and this paper, and a highlight of the pros and cons of each idea. Our conclusion is different from the negative of Norberg [19].…”

Section: Introductionmentioning

confidence: 92%

“…In addition to the work of Norberg [19], the question has also been investigated by e.g. Christiansen and Niemeyer [6] and Buchardt [4].…”

Section: Forward Transition Ratesmentioning

confidence: 99%

“…Buchardt The definition of forward transition rates studied by Buchardt [4] is for all practical purposes, see also Buchardt [4] Lemma 4.3, equivalent to setting…”

Section: Alternative Definitions From the Literaturementioning

confidence: 99%

“…As it turned out, this was not enough to kill the idea itself. Lately, Christiansen and Niemeyer [6] and Buchardt [4] have proposed different generalizations with individual characteristics.…”

Section: Introductionmentioning

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: Proof See Appendix Amentioning

confidence: 92%

Section: Introductionmentioning

confidence: 92%

“…In addition to the work of Norberg [19], the question has also been investigated by e.g. Christiansen and Niemeyer [6] and Buchardt [4].…”

Section: Forward Transition Ratesmentioning

confidence: 99%

“…Buchardt The definition of forward transition rates studied by Buchardt [4] is for all practical purposes, see also Buchardt [4] Lemma 4.3, equivalent to setting…”

Section: Alternative Definitions From the Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Forward transition rates

Buchardt¹,

Furrer

Steffensen

2019

Finance Stoch

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Chapter VII: Special Studies in Life Insurance

Asmussen

Steffensen

2020

Risk and Insurance

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On the calculation of prospective and retrospective reserves in non-Markov models

Christiansen

2021

Eur. Actuar. J.

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Almost all life and health insurance models in the actuarial literature use either a Markov assumption or a semi-Markov assumption. This paper shows that non-Markov modelling is also feasible and presents suitable numerical and statistical tools for the calculation of prospective and retrospective reserves. A central idea is to base the calculation of reserves on forward and backward transition rates. Feasible estimators for the forward transition rates have been recently suggested in the medical statistics literature. This paper slightly extends them according to insurance needs and newly introduces symmetric estimators for backward transition rates. Only few adjustments are actually needed in the classical insurance formulas when switching from Markov modelling to as-if-Markov evaluations in order to avoid model risk.

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Kolmogorov’s forward PIDE and forward transition rates in life insurance

Cited by 6 publications

References 15 publications

Forward transition rates

Forward transition rates

Chapter VII: Special Studies in Life Insurance

On the calculation of prospective and retrospective reserves in non-Markov models

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