Quick search | Browse volumes | |

XIV: 18, 152-160, LNM 784 (1980)

**ÉMERY, Michel**

Compensation de processus à variation finie non localement intégrables (General theory of processes, Stochastic calculus)

First an example is given of a local martingale $M$ and an unbounded previsible process $H$ such that $H.M$ exists in the sense of 1126 and 1415, but is not a local martingale. This leads to a natural enlargement of the class of local martingales, which turns out to be the same suggested by Chou in 1322 under the name of class $(\Sigma_m)$. Once the class has been so extended, the operation of previsible compensation can be extended to a class of processes with finite variation, but not locally integrable variation, and the class of special semimartingales can be also enlarged

Comment: This class has found recently a natural use in mathematical finance (Delbaen-Schachermayer 1997). Using the language of L. Schwartz 1530, it is the intersection of the set of (usual) semimartingales with the set of formal martingales

Keywords: Local martingales, Stochastic integrals, Compensators

Nature: Original

Retrieve article from Numdam

Compensation de processus à variation finie non localement intégrables (General theory of processes, Stochastic calculus)

First an example is given of a local martingale $M$ and an unbounded previsible process $H$ such that $H.M$ exists in the sense of 1126 and 1415, but is not a local martingale. This leads to a natural enlargement of the class of local martingales, which turns out to be the same suggested by Chou in 1322 under the name of class $(\Sigma_m)$. Once the class has been so extended, the operation of previsible compensation can be extended to a class of processes with finite variation, but not locally integrable variation, and the class of special semimartingales can be also enlarged

Comment: This class has found recently a natural use in mathematical finance (Delbaen-Schachermayer 1997). Using the language of L. Schwartz 1530, it is the intersection of the set of (usual) semimartingales with the set of formal martingales

Keywords: Local martingales, Stochastic integrals, Compensators

Nature: Original

Retrieve article from Numdam