Continuous formula for the price of an asset paying one terminal dividend?

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:

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:

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