# Give the formula for following resulting portfolio process

Consider the continuously sampled a derivative security with payoff function
$$V(T) = \frac {\int_0^TS(u)du}T -K$$ but assume now that the interest rate is $$r=0$$. Find an initial capital $$X(0)$$ and a nonrandom function $$\gamma(t),0\leq t \leq T$$ , which will be the number of shares of risky asset held by our portfolio so that $$X(T) = V(T)$$ still holds. Give the formula for resulting process $$X(t)$$ in term of underlying asset price and K. I don't know how to start these type of questions. I started by finding $$V(0)$$ but couldn't do much afterwards. Can someone solve it.

• This looks a lot like a homework question. Insofar as you're asking for help with homework, you're likely to get more constructive feedback if you provide details on what you've tried so far and ask specific questions rather than asking 'Can someone solve it'. – Chris Apr 9 at 22:31