Consider a self-financing trading strategy of a portfolio with a dividend paying asset and a money market
Consider a self-financing trading strategy of a portfolio with a dividend paying asset and a money market account over the time horizon [0,T ]. Under the risk neutral measure Q, let the dynamics of the asset price St be governed by
where q is the dividend yield, q = r. We adopt the trading strategy of holding nt units of the asset at time t, where
Let Xt denote the portfolio value at time t, whose dynamics is then given by
The initial portfolio value X0 is chosen to be
where Z∗t = Zt − σt is a Brownian process under Q∗-measure with eqtSt as the numeraire. Note that the price function of the fixed strike Asian call option with strike X is given by
with u(y,T ) = max(y, 0).
Step by Step Answer: