Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.

and and Very very grateful!
Transcribed Image Text:2. Let Bt be the standard Brownian motion and Ft = σ(Bs, s≤ t). Deduce exp(0Bt - 10²+) is a martingale with respect to {Ft;t > 0} to from the fact that Zt = show that both B² – t and B¾³ – 3tB₁ are martingales with respect to {Ft;t ≥ 0}. (Hint: t Use Taylor expansion of Z as a function of 0.)

Question

Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.

and and Very very grateful!

2.
Let Bt be the standard Brownian motion and Ft = σ(Bs, s≤ t). Deduce
exp(0Bt - 10²+) is a martingale with respect to {Ft;t > 0} to
from the fact that Zt
=
show that both B² – t and B¾³ – 3tB₁ are martingales with respect to {Ft;t ≥ 0}. (Hint:
t
Use Taylor expansion of Z as a function of 0.)

Accepted Answer

Answered: Image /qna-images/answer/2c9c4145-e324-497c-9d3a-5bc32f1d99fe.jpg