Homework$-$Due: $11$:$59$pm$,$ Monday$-29$th April, $2024$

Consider the stock price process $\{V(t),t0\}$ defined as $V(t)=V(0)e^{B(t)},t0.$ Given that the initial value of the stock is $$30$ and the volatility parameter $=2.$ The investor plans to sell the stock when it reaches $$40$ or when it falls to $$25.$

$($a$)$ What is the probability that the investor ends up selling at a loss?

$($b$)$ What is the probability that the investor ends up selling at a profit?

$($c$)$ What is the expected net profit from following this strategy?

$($d$)$ What is the expected time for the investor to sell the shares?