Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 202 / 2 / c / i / Solution

The martingale product identity says that $N_t{K}_t-[N,K{]}_t$ is a martingale. Passing to the terminal values of the square-integrable martingales and using $N_0=K_0=0$ givesThe quadratic covariation identity for a stochastic integral isApplying the same product identity to $H\cdot M$ and $K$ therefore gives