I have been trying to come up with ways to come up with an answer for a question we got in my class of "Asset Pricing Theory". The question is as follows:

"Write the price of the asset at time t in terms of the dividends at time t, $D_t$. The answer is also a function of the difference between $T$ (the time of the final dividend payment) and $t$."

We are given the following information:

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We also know that the dynamics of consumption is given as:

$dc_t = c_t[\mu_[ct]dt+\sigma_[ct]^Tdz_t$

and that the dynamics of the dividends are given as:

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I am a bit at a loss, as to where to start? Can someone perhaps provide some guidelines?


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