integration - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive...

5
9 STOCHASTIC INTEGRATION RECEP

Upload: others

Post on 23-Jun-2020

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic

9 STOCHASTICINTEGRATIONRECEP

Page 2: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic

TO DERIVE THE HTB EQUATION WE NEEDED

TAYLOR EXPANSIONSCHAIN RULE

WE RECAP THE SAME FOR STOCHASTIC INTEGRAL

Page 3: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic

STOCHASTICINTEGRAL INDEPENDENTGAUSSIANINCREMENTS LINEvariation

FOR BROWNIAN MOTION sewor

SO STOCHASTIC

INTEGRAL

Page 4: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic

STOCHASTICDIFFERENTIAL EQUATIONS

DEFINE

LET 8 so

THIS GIVES US TAYLOR APPROXIMATIONS FOR 5D Es

Page 5: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic

ITISFOR MULA For OUR SDE FROM BEFORE

THIS GIVES US A CHAINRULE FOR S D E s