Facoltà di scienze economiche

On the structure of finitely additive martingales

Cassese, Gianluca

Finitely additive martingales are the counterpart of finitely additive measures over filtered probability space. We study the structure of the Yosida Hewitt decomposition in such setting and obtaing a full characterisation. Based on this result we introduce a “conditional expectation” operator for finitely additive measures which has some properties in common with ordinary conditional... More

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    Summary
    Finitely additive martingales are the counterpart of finitely additive measures over filtered probability space. We study the structure of the Yosida Hewitt decomposition in such setting and obtaing a full characterisation. Based on this result we introduce a “conditional expectation” operator for finitely additive measures which has some properties in common with ordinary conditional expectation. We address then the problem of computing the expectation of random elements generated by a given class of stochastic processes. On the basis of a notion of coherence for processes, akin to the no arbitrage principle in mathematical finance, we give conditions under which such expectation may be computed explicitely.