In a fully general setting, we study the relation between martingale spaces under two locally absolutely continuous probabilities and prove that the martingale represen- tation property (MRP) is always stable under locally absolutely continuous changes of probability. Our approach relies on minimal requirements, is constructive and, as shown by a simple example, enables us to study situations which cannot be covered by the existing theory.
Martingale spaces and representations under absolutely continuous changes of probability
Claudio Fontana
2019
Abstract
In a fully general setting, we study the relation between martingale spaces under two locally absolutely continuous probabilities and prove that the martingale represen- tation property (MRP) is always stable under locally absolutely continuous changes of probability. Our approach relies on minimal requirements, is constructive and, as shown by a simple example, enables us to study situations which cannot be covered by the existing theory.
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