 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2011/b/6/a/solution

Under the physical probability, the stock has mean

E S_{t} = 50 e^{0.1 t}

. Nonnegativity permits interchanging expectation and integration in the accumulated dividends. Hence

E X_{T} = 50 e^{0.1 T} + 0.01 \int_{0}^{T} 50 e^{0.1 t} e^{0.05 (T - t)} d t = 50 e^{0.1 T} + 10 (e^{0.1 T} - e^{0.05 T}) .

Therefore

E X_{T} = 60 e^{0.1 T} - 10 e^{0.05 T} pounds .

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