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Title: Stochastic processes defined from a Lagrangian
Authors: De Vylder, FE ×
Goovaerts, Marc
Kaas, Robert #
Issue Date: 1992
Series Title: Insurance: Mathematics & Economics vol:11 issue:1 pages:55-69
Abstract: In a previous work by Goovaerts, De Vylder, and Kaas (1992), an intuitive approach was given to the problem of solvency and equalization leading to analytical results. A distribution describing the probability of a trajectory of the surplus between 2 fixed time points was derived, given the initial value of the surplus as well as a projection for the final value of the surplus at the end of the interval. The joint distribution describing the probability distribution of some intermediate points was derived in such a way that its mode coincides with a trajectory, given in advance by means of a 2nd-order differential equation. Consequently, a stochastic description was given connecting some probabilities to all possible trajectories. The stochastic model constructed in this way is such that the average trajectory coincides with the trajectory giving the mode. A rigorous introduction of the results in case of quadratic Lagrangian functions is presented. An extension is given to the case where only the starting value of the surplus is given as well as the end of the time interval considered, but not the final value of the surplus
ISSN: 0167-6687
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Research Center Insurance, Leuven
× corresponding author
# (joint) last author

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