Following is given,
$dS(t)= (r-\delta)S(t)dt+\sigma S(t)dW(t)$
where, $r$ is the risk-free interest rate, $\delta$ the continous dividend yield $\sigma$ is the stock asset volatility and $W$ brownian motion.
By solving the SDE that is the money account B and applying Itô's lemma on the stock dynamic S I get,
I know further that the No Arbitrage price is defined as,
Can I somehow cancel out B(T) since it is deterministic? How do I calculate the expectation of a maximum with a brownian motion W?
I am new to probability theory, financial mathematics and stochastic calculus. Would appreciate step-wise guidance. Thank you!