A stochastic version of Thiele's differential equation

DOI10.1080/03461238.1993.10413910zbMath0783.62085OpenAlexW2019197114WikidataQ115297968 ScholiaQ115297968MaRDI QIDQ3142171

Christian Max Møller

Publication date: 12 December 1993

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461238.1993.10413910

zbMATH Keywords

stochastic differential equationnumerical examplepoint processlife insurancemartingale representationssemi-Markov modelThiele's differential equation

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

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Multistate models in health insurance, A counting process approach to stochastic interest, Dynamics of state-wise prospective reserves in the presence of non-monotone information, Kolmogorov’s forward PIDE and forward transition rates in life insurance, Cash flows and policyholder behaviour in the semi-Markov life insurance setup, Markov models and Thiele's integral equations for the prospective reserve, Aspects of prospective mean values in risk theory, Thiele's differential equation with stochastic interest of diffusion type, Addendum to Hattendorff's Theorem and Thiele's Differential Equation Generalized, SAJ 1992, 2–14, Time-dynamic evaluations under non-monotone information generated by marked point processes, Nonlinear reserving and multiple contract modifications in life insurance, Stochastic interest rate in life insurance: The principle of equivalence revisited

Cites Work

• Point processes and queues. Martingale dynamics
• Hattendorff's theorem and Thiele's differential equation generalized
• Numerical evaluation of Markov transition probabilities based on the discretized product integral
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