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Dynamics of state-wise prospective reserves in the presence of non-monotone information. (English) Zbl 1460.91216

Summary: In the presence of monotone information, the stochastic Thiele equation describing the dynamics of state-wise prospective reserves is closely related to the classic martingale representation theorem. When the information utilized by the insurer is non-monotone, the classic martingale theory does not apply. By taking an infinitesimal approach, we derive a generalized stochastic Thiele equation that allows for information discarding. En passant, we solve some open problems for the classic case of monotone information. The results and their implication in practice are illustrated via examples where information is discarded upon and after stochastic retirement.

MSC:

91G05 Actuarial mathematics
60G48 Generalizations of martingales
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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