Choosing Constrained Actions from Price Forecasts

Summary

The document asks how to turn a sequence of predicted future prices into an optimal trading plan for a single asset and cash pair. Its proposed setting removes bid–ask spreads, restricts the trader to long-only exposure, and fixes the asset position size, so decisions amount to entering, holding, or exiting a position. The suggested procedure is to optimize a sequence of actions over a finite horizon, then execute only the first action and repeat as forecasts update.

The central issue is whether optimizing over feasible position changes is more complicated than optimizing over trade sequences in the referenced paper. The document offers no answer, empirical evidence, or implementation details; it is a question seeking guidance. Any practical formulation would depend on the paper’s objective, how forecasts are treated, and constraints such as transaction costs, position limits, and the need to avoid invalid sequences. Those considerations are outside the document’s simplified setup.

Key ideas

• The setup assumes one asset, no bid–ask spread, long-only exposure, and a fixed trade size.
• The proposed method optimizes actions across a forecast horizon but executes only the first action.
• Feasible action sequences must respect position constraints, such as avoiding purchases while already holding the allowed unit.
• The document raises, but does not resolve, how this constrained problem compares with the paper’s trade-sequence optimization.

Tags

# Am I overcomplicating this approach to optimal actions based on a forecast?


# Am I overcomplicating this approach to optimal actions based on a forecast?












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?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.