I am new to stochastic control and I need your help! Suppose that we are a trader and we are trading based two sources of signal. One comes from the stock's flow of dividends as well as another trader's demand. Assume that the dividend flow moves as $$ dD_t = \mu_D dt + \sigma_D dZ^1_t $$ where $Z^i_t$ denotes a standard Wiener process. Also suppose that the other trader trades randomly and demands on the interval $[t,t+dt)$ the amount $dY_t$. Indeed $Y_t$ denotes the cumulative purchased shares the other trader holds. Also assume that

$$ dY_t = \mu_Z dt + \sigma_Z dZ^2_t $$

For me it is both intuitive and technically robust to assume that we can trade as a function of the other trader's demand. I mean if we trade like $dX_t = -dY_t$ then we are spanning the filtration made by the other trader's movements. That is to say, my demand has an increment with $dZ^2_t$ in it. Am I able to do a trade based on the "flow" variable $D_t$ as well? What is the intuition? What technical assumption makes it possible?

For example if I trade just the opposite direction of the other trader and just the magnitude of dividends paid then my trade at $[t,t+dt)$ will be $$D_t dt-dY_t$$. But can I reach a trading policy which has the form $$KdZ_t^1$$?


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