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  .
The information dynamics in finance and insurance applications is usually modeled by a filtration . This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale representations. We present a general theory that extends classical martingale representations to non-monotone information generated by marked point processes. The central idea is to focus only on those properties that martingales and compensators show on infinitesimally short intervals. While classical martingale representations describe innovations only, our representations have an additional symmetric counterpart that quantifies the effect of information loss . We exemplify the results with examples from life insurance and credit risk .
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classical concept of martingales and compensators bases on the monotony of filtrations
information dynamics in finance and insurance applications is usually modeled by a filtration
R
the situation where innovations can have an expiry date
situations where information restrictions apply
R
becomes
may become
A
A fundamental tool for calculating and managing risks in finance and insurance are martingale representations. We present a general theory that extends classical martingale representations to non-monotone information generated by marked point processes.
R
Infinitesimal martingale representations are derived that extend
While
D
to non-monotone information. While the classical representations
R
the extended
our
A
. We exemplify the results with examples from life insurance and credit risk