Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 29K / b

Table of contents
- Solution b

Solution

If

θ_{n}

shares are held during period

n

, the remaining wealth

X_{n - 1} - θ_{n} S_{n - 1}

is in the bank account. Self-financing therefore gives

X_{n} = θ_{n} S_{n} + (1 + r) (X_{n - 1} - θ_{n} S_{n - 1}),

which rearranges to the required equation.

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