Hattendorff's theorem and Thiele's differential equation generalized

DOI10.1080/03461238.1992.10413894zbMath0755.62081OpenAlexW2068764135WikidataQ115297986 ScholiaQ115297986MaRDI QIDQ4025272

Ragnar Norberg

Publication date: 18 February 1993

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

Full work available at URL: https://doi.org/10.1080/03461238.1992.10413894

zbMATH Keywords

martingaleslife insurancecounting processpayment streamsHattendorff's theoremoptional samplingcontinuous time Markov chain modelstochastic Thiele's differential equation

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (21)

Differential equations for moments of present values in life insurance ⋮ Nonlinear reserving in life insurance: aggregation and mean-field approximation ⋮ Dynamics of state-wise prospective reserves in the presence of non-monotone information ⋮ Integral and differential equations for the moments of multistate models in health insurance ⋮ Product pricing and solvency capital requirements for long-term care insurance ⋮ Converting retirement benefit into a life care annuity with graded benefits ⋮ Markov models and Thiele's integral equations for the prospective reserve ⋮ Transaction time models in multi-state life insurance ⋮ Stochastic analysis of a portfolio of endowment insurance policies ⋮ Thiele's differential equation with stochastic interest of diffusion type ⋮ Hattendorff's theorem for non-smooth continuous-time Markov models. I: Theory ⋮ Mean-field reflected backward stochastic differential equations ⋮ Indicator Function and Hattendorff Theorem ⋮ A no arbitrage approach to Thiele's differential equation ⋮ Ragnar Norberg (1945–2017): an actuary of a unique kind ⋮ 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 ⋮ Multivariate higher order moments in multi-state life insurance ⋮ Principle of equivalent utility and universal variable life insurance pricing ⋮ A stochastic version of Thiele's differential equation

Cites Work

• Payment Measures, Interest, and Discounting
• Martingales in life insurance
• Hattendorff's theorem for a continuous-time Markov model
• Hattendorff's Theorem: A Markov chain and counting process approach
• Reserves in Life and Pension Insurance
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