Let X X be a semi-martingale. Check that the solution of the S D E d S
Question:
Let X be a semi-martingale. Check that the solution of the SDEdSt=St−(b(t)dt+σ(t)dXt) is
St=S0exp(Ut)Πt
where
Ut=∫t0σ(s)dXs+∫t0b(s)ds−12∫t0σ2(s)d⟨Xc⟩sΠt=∏0<s≤t(1+σ(s)ΔXs)exp(−σ(s)ΔXs).
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Related Book For
Mathematical Methods For Financial Markets
ISBN: 9781447125242
1st Edition
Authors: Monique Jeanblanc, Marc Yor, Marc Chesney
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