📘 stochastic calculus

1. The problem is to understand what stochastic differential equations (SDEs) are and how they are used. 2. A stochastic differential equation is a differential equation in which o

1. The problem is to verify the derivation that the discounted stock price $\tilde{S}_t = e^{-rt}S_t$ is a martingale under the risk-neutral measure $Q$ given the SDE for $S_t$: $$