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Larsson, Martin. Abstract Article info and citation First page References Abstract When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths.

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On the hedging of options on exploding exchange rates. Finance Stoch.

## Probabilities and Potential, B, Volume 72

You have access to this content. You have partial access to this content. Given a Brownian motion process W t and a harmonic function f , the resulting process f W t is also a martingale. The intuition behind the definition is that at any particular time t , you can look at the sequence so far and tell if it is time to stop. An example in real life might be the time at which a gambler leaves the gambling table, which might be a function of their previous winnings for example, he might leave only when he goes broke , but he can't choose to go or stay based on the outcome of games that haven't been played yet.

That is a weaker condition than the one appearing in the paragraph above, but is strong enough to serve in some of the proofs in which stopping times are used. The concept of a stopped martingale leads to a series of important theorems, including, for example, the optional stopping theorem which states that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial value.

From Wikipedia, the free encyclopedia. For the martingale betting strategy, see martingale betting system.

## V3F1 Stochastic Processes

Main article: Stopping time. Azuma's inequality Brownian motion Doob martingale Doob's martingale convergence theorems Doob's martingale inequality Local martingale Markov chain Martingale betting system Martingale central limit theorem Martingale difference sequence Martingale representation theorem Semimartingale.

Money Management Strategies for Futures Traders. Wiley Finance. Electronic Journal for History of Probability and Statistics.

Archived PDF from the original on Retrieved Probability and Random Processes 3rd ed. Oxford University Press.

## Larsson : Filtration shrinkage, strict local martingales and the FĂ¶llmer measure

Stochastic processes. Bernoulli process Branching process Chinese restaurant process Galtonâ€”Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding Biased Maximal entropy. List of topics Category.