The classical concept of martingales and compensators bases on the monotony of filtrations. This paper looks at the situation where innovations can have an expiry date such that the information dynamics becomes non-monotone. By focussing on the properties that martingales and compensators show on infinitesimally small intervals, the classical martingale concept is extended and corresponding martingale representations are developed. The extended martingale representations lead to a new type of Thiele-Feynman-Kac equations, which are exemplarily discussed for two example from life insurance mathematics .
The classical concept of martingales and compensators bases on the monotony of filtrations. This paper looks at the situation where innovations can have an expiry date such that the information dynamics becomes non-monotone. By focussing on the properties that martingales and compensators show on infinitesimally small intervals, the classical martingale concept is extended and corresponding martingale representations are developed. The extended representations make it possible to generalize Thiele's equation in insurance mathematics to situations where information restrictions apply .
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martingale representations lead to a new type of Thiele-Feynman-Kac equations, which are exemplarily discussed for two example from life insurance mathematics
representations make it possible to generalize Thiele's equation in insurance mathematics to situations where information restrictions apply