Dynamics of state-wise prospective reserves in the presence of non-monotone information

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