Bathke, Theis (2025) Non-Markov modeling in life insurance. PhD, Universität Oldenburg.

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Abstract

This thesis investigates advances in non-Markov models, focusing on two-dimensional extensions of conditional forward transition rates and their applications in life insurance. The concept of conditional forward transition rates, originally developed to improve reserve estimation by eliminating the need for the Markov assumption, enables the calculation of conditional expected values. The newly developed two-dimensional conditional transition rates are used to calculate second-order conditional moments, which are crucial for risk analysis in actuarial applications. To further support this framework, an estimator for two-dimensional conditional transition rates is introduced, combining the theory of bivariate survival functions with the theory of landmark Nelson-Aalen and landmark Aalen-Johansen estimation. These two-dimensional conditional transition rates prove useful not only for calculating second-order moments but also for capturing the intertemporal dependency of path-dependent cash flows, such as those resulting from incidental policyholder behavior upon contract modifications.Furthermore, an alternative approach to reserve estimation for policies with path-dependent cash flows is examined. This method uses scaled transition rates and scaled probabilities, which capture the stochastic nature of the payment functions by incorporating it as a scaling factor into the Aalen-Johansen estimation. This estimation procedure is also beneficial for analyzing more general stochastic payments, such as those involving stochastic interest rates.

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Nicht-Markovsche Modellierung in Lebensversicherungen

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This thesis investigates advances in non-Markov models, focusing on two-dimensional extensions of conditional forward transition rates and their applications in life insurance. The concept of conditional forward transition rates, originally developed to improve reserve estimation by eliminating the need for the Markov assumption, enables the calculation of conditional expected values. The newly developed two-dimensional conditional transition rates are used to calculate second-order conditional moments, which are crucial for risk analysis in actuarial applications. To further support this framework, an estimator for two-dimensional conditional transition rates is introduced, combining the theory of bivariate survival functions with the theory of landmark Nelson-Aalen and landmark Aalen-Johansen estimation. These two-dimensional conditional transition rates prove useful not only for calculating second-order moments but also for capturing the intertemporal dependency of path-dependent cash flows, such as those resulting from incidental policyholder behavior upon contract modifications. Furthermore, an alternative approach to reserve estimation for policies with path-dependent cash flows is examined. This method uses scaled transition rates and scaled probabilities, which capture the stochastic nature of the payment functions by incorporating it as a scaling factor into the Aalen-Johansen estimation. This estimation procedure is also beneficial for analyzing more general stochastic payments, such as those involving stochastic interest rates.

Item Type:	Thesis (PhD)
Uncontrolled Keywords:	Life and health Insurance, non-Markov modeling, Markov modeling, Landmark estimation, higher-order Moments of insurance cash flows
Subjects:	Science and mathematics > Mathematics
Divisions:	Faculty of Mathematics and Science > Institute for Mathematics (IfM)
Date Deposited:	11 Feb 2025 10:12
Last Modified:	11 Feb 2025 10:12
URI:	https://oops.uni-oldenburg.de/id/eprint/7126
URN:	urn:nbn:de:gbv:715-oops-72070
DOI:
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