I have been attempting to implement a simplified version of the model used in this paper which, given a forecast of future data, provides an optimal way of acting on it by choosing an optimal sequence of actions out to some horizon, $H$, and only executing the first, but am wondering if I am overcomplicating things for my goals.

Let's say that we are working with an exchange with a single asset/cash pair.

To simplify things, we assume that there is no bid/ask spread.

We also require that our agent is long-only and has a fixed investment/order size, e.g. our agent can only be holding all cash or cash and a fixed amount of the asset at any time.

We let $a=-1$ denote selling 1 unit of the asset, $a=0$ denote doing nothing, and $a=1$ denote buying 1 unit of the asset,

Given that we are at $t=0$ and are holding only some sufficient amount of cash to buy a unit of the asset for $p_0$, how do we choose an action ($a=0 \text{ or }a=1$) by finding an optimal sequence of decisions given predictions ($\hat{p}_1, \dots, \hat{p}_H$) and executing the first, as described in the paper?

Am I creating a more difficult/different problem by optimizing over the space of valid action sequences (e.g. the sequence can only contain a -1 after a 1, can't contain consecutive 1's, etc.) instead of over the space of sequences of trades as in the paper? Specifically, is there an easier way that something like this would be implemented in practice?



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