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 Mar 4 awarded Revival Dec 11 awarded Yearling Jun 30 revised Ito's formula for Jump process added 353 characters in body Jun 30 comment Ito's formula for Jump process No, it's just arithmetic...The poisson jumps by 1, so $B_t$ jumps correspondingly. Jun 30 comment Ito's formula for Jump process @Behrouz thoughts? Jun 30 answered Ito's formula for Jump process Jun 30 comment Reflection Principle Use the fact that $\widetilde{W}_t := W_{t \vee \tau} - W_\tau$ is a Brownian Motion independent of $W_\tau$ by the strong markov property, and that subsequently so is $-\widetilde{W}_t$. Jun 30 comment Ito's formula for Jump process @Behrouz I think you can use the product rule of ordinary calculus. The jump term itself doesn't require calculus at all. Jun 30 comment Ito's formula for Jump process Ito's Lemma isn't really necessary, since Poisson processes have finite variation. May 27 answered Multidimensional Ito's Lemma for Vector-Valued functions Apr 27 comment Why the expected return rate of a stock has nothing to do with its option price? Because the pricing is by no arbitrage. Jan 8 revised Strictly local martingales: what is the intuition behind them? added 3 characters in body Jan 8 answered Strictly local martingales: what is the intuition behind them? Dec 11 awarded Yearling Oct 9 comment Show that $E[B_t|\mathscr{F}_s] = B_s$ Yep, totally correct. Oct 9 comment Show that $E[B_t|\mathscr{F}_s] = B_s$ Technical point: the pde condition on f only guarantees that it will be a local martingale. Integrability has to be checked separately. Sep 30 awarded Explainer Sep 24 awarded Autobiographer May 22 comment Existence of a hedging portfolio and martingale property ok, so the supermartingale is the value process corresponding to an american option. if i understand your question, then at a theoretical level, the answer is yes: doob-meyer decomposition to split the supermartingale into a martingale and decreasing process, and then martingale representation to get a hedging strategy for the martingale part. May 22 comment Existence of a hedging portfolio and martingale property what do you mean by a super martingale price process?