Stock market in a DSGE model

Hi, I wonder if there is a well-recognized DSGE model with a stock market? What I mean is that people can buy and sell stocks in it, and the stock price might follow the deifinition in finance field (Brownian motion) or not.
If no, what do you think is the difficulties to built this model?
Every opinion is welcomed. Thanks!

I am not aware of such a model. Most DSGE models are representative agent models that only determine the equilibrium price in a no-trade equilibrium. See e.g. DSGE_mod/Jermann_1998 at master · JohannesPfeifer/DSGE_mod · GitHub

Thanks for answering, Professor jpfeifer. What confuses me is that why stock market can not be modeled like a product market? You see, they can be both traded and have their own prices, and their prices are determined by the demand and supply. What do you think is the difficuties?

The model references above does that. There is a normalized supply of shares and there is a demand function for shares. But the equilibrium still features no trades and is therefore far from typical finance models that have noise traders.

I see. Your opinion values a lot! Thanks again! Professor.