 Solution

ID: past-exam-of-the-mathematical-models-of-financial-derivatives-course-of-the-university-of-oxford/2023/3/b/solution

e^{αu}

d (e^{αu} x_{u}) = α μ e^{αu} d u + σ e^{αu} d Z_{u} .

Integrate from

t

T

and multiply by

e^{- α T}

to obtain

x_{T} = x_{t} e^{- α (T - t)} + μ (1 - e^{- α (T - t)}) + σ e^{- α T} \int_{t}^{T} e^{αu} d Z_{u} .

 New to topics? Read the docs here!