# Consider a self-financing trading strategy of a portfolio with a dividend paying asset and a money market

## Question:

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 S_{t} 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 X_{t} denote the portfolio value at time t, whose dynamics is then given by

The initial portfolio value X_{0} is chosen to be

where Z^{∗}_{t} = Z_{t} − σt is a Brownian process under Q^{∗}-measure with e^{qt}S_{t} 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:

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