Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 211 / 1 / f / Solution

Normalize the self-financing strategy $\eta$ by definingPart e makes this well-defined, andMoreover,Both $K$ and $L$ have constant unit price and predictable dividends. Their difference has zero price and predictable dividend ${\xi }^K-{\xi }^L$. If that dividend were nonzero with positive probability, taking its known sign would produce an arbitrage. Therefore ${\xi }^K={\xi }^L$, proving