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1d
revised Ito's formula for Jump process
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1d
comment Ito's formula for Jump process
No, it's just arithmetic...The poisson jumps by 1, so $B_t$ jumps correspondingly.
1d
comment Ito's formula for Jump process
@Behrouz thoughts?
1d
answered Ito's formula for Jump process
1d
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 $-\widetilde{W}_t$.
1d
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.
2d
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 Creating correlated Brownian motions from independent ones
Just compute the quadratic variation of each process.
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?
May
18
comment Difference betweem martingale property and adapted filteration
Also, this is something I think about from time to time. You can definite martingality intrinsically, by taking the filtration to be the natural one generated by $X$. Does this mean that martingality is an intrinsic property?