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 .
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. The central idea is to focus only on those properties that martingales and compensators show on infinitesimally short intervals. Infinitesimal martingale representations are derived that extend classical martingale representations to non-monotone information. While the classical representations describe innovations only, the extended representations have an additional symmetric counterpart that quantifies the effect of information loss .
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By focussing on the
The central idea is to focus only on those
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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
short intervals. Infinitesimal martingale representations are derived that extend classical martingale representations to non-monotone information. While the classical representations describe innovations only, the extended representations have an additional symmetric counterpart that quantifies the effect of information loss