Beschreibung:
It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications.
1. Spaces, Laws and Limits. 2. Stochastic Processes. 3. Martingales. 4. Strong Supermartingales. 5. Optional Martingales. 6. Optional Supermartingales Decomposition. 7. Calculus of Optional Semimartingales. 8. Optional Stochastic Equations. 9. Optional Financial Markets. 10. Defaultable Markets on Unusual Space. 11. Filtering of Optional Semimartingales. Bibliography. Index.