From Forecast to Position: Order-Book Signals, Market Impact, and Causal Trading

An order-book forecast becomes a trading decision through costs, constraints and the information available when the position is chosen. This paper derives loss identities and certificates for that conversion. Positive curvature gives a convex-conjugate loss and quadratic sensitivity; purely proportional costs create threshold decisions with different error rates. Forecast intervals admit exact scalar minimax decisions. Finite marked-event models transfer errors in book dynamics, price marks, filtering and state reduction into forecast and decision error. Information unavailable to the trader has a separate cost. The analysis distinguishes observation loss, latency and implementation error, and extends the comparison to adapted trading trajectories with impact and constraints. A baseline-relative extension converts conditional-mean uncertainty into a certified position change. It gives an explicit portfolio no-trade region and a scalar rule in which transaction costs and forecast uncertainty widen the same threshold. Under simultaneous mean coverage and a conditional exponential-moment bound, a normal-mixture argument transfers conditional decision gains into a time-uniform lower bound on realized outcomes. In a one-period cell whose joint fill/return law does not depend on the attempted order, a random-fill extension identifies the joint moments needed to convert a price forecast into an order. A joint-moment uncertainty set yields robust continuous and lot-grid orders, while pathwise fill bounds enforce portfolio exposure. A bounded-outcome mixture certificate then transfers certified conditional gains to realized random-filled outcomes under explicit sequential assumptions. Independent synthetic calculations check the identities, optimizers and sequential boundary. Forecast-set coverage, executable costs and conditional tail assumptions remain requirements for a market application. The results concern declared objectives and exogenous book laws, not empirical profitability or a solution to counterfactual market impact.