I am reading the paper High Frequecy Trading in a Limit Order Book by Sasha Stoikov and Marco Avellaneda. There is a point that I am having trouble understanding.
The authors give a definition of the of the optimization problem that they want to solve.
My question is, why is $\theta$ not a function of cash that I have generated while trading and only depends on the terminal condition in terms of the numbers of stocks held?
I have only little understanding of Hamilton-Jacobi-Bellman equation. Not sure if some of the results follow from there.