From conjectural income to probabilistic forecasting [Keynote Speaker]

The determination of the income, the operating capital, and the net cash flow of the going concern has long been articulated, within the European accounting tradition, through Financial and Management Accounting equations, in which such magnitudes are apprehended as conjectural quantities. In their canonical form these equations are deterministic and, for the most part, linear, and they yield point estimates of income, capital, and net cash-flow; yet the real conditions of the firm and of its environment are pervaded by aleatory events, so that the punctual representation, however rigorous, cannot of itself accommodate the uncertainty that attends every forecast, plan and program. The present contribution advances a single, unifying thesis: that the selfsame summary equation, once recast in vector–matrix form and thereafter reformulated stochastically, is rendered operable by means of artificial intelligence and, more precisely, of machine learning. The claim is not that a new model supplants the received one, but rather that the architecture bequeathed by European and American Scholars already contains the probabilistic and computational apparatus that contemporary methods render explicit. The argument proceeds through four movements. Under first-best conditions, planned income and the margin of contribution are examined by way of what-if and scenario analysis, the elementary response to risk in prediction and programming. The passage from the scalar to the vector then arrays the firm's productive alternatives as a family of flexible budgets, whose summary values (revenues, variable costs, contribution margins, fixed costs and income) become objects of linear and multilinear algebra and, for that very reason, tractable by business software. Relaxing the assumption of certainty, the conditions of the firm are subsequently redefined through subjective probability distributions: the expected value of income is derived under a Bayesian criterion, arranged in a payoff matrix over the states of nature, and discounted so as to yield the economic capital as the present value of the expected stream of future income. The recourse to Prospect Theory, as against Expected Utility Theory, motivates in turn the adoption of asymmetric loss functions in place of the mean alone. Upon this foundation, the paper establishes a systematic correspondence between the elements of the equations and the instruments of machine learning. Machine learning is thus construed as the computational realization of the accounting logic, and not as its surrogate. The exposition closes with a necessary caveat (that the firm, as an ultra-complex unity, does not admit of optimization in its entirety, so that only sub-optimal techniques applied to its constituent parts are warranted), and it indicates avenues for further inquiry, among them long-range planning horizons, the notion of deterministic chaos, and the empirical validation of the proposed framework.