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Hard · Stochastic Calculus · Quant Trader interview question · Radon-Nikodym Derivative, Change of Measure, Girsanov's Theorem, Brownian Motion, Stochastic Calculus
Suppose you are working on a stochastic control problem, and you want to change the probability measure under which a Brownian motion is defined. Specifically, you start with a Brownian motion $W_t$ under a probability measure $P$, and you know that under a new probability measure $Q$, the process $W_t$ is a Brownian motion with a constant drift $\mu$, i.e., $W_t + \mu t$ is a standard Brownian motion under $Q$. What is the Radon-Nikodym derivative $dQ/dP$ (evaluated at time $T$) that allows you