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Abstract
This paper probes into the foundations of conventional accounting measurements in order to construct a relatively simple axiom system on which a purely mathematical measurement system can be erected and thus provide a consistent basis for examining pertinent aspects of conventional accounting practices. […] We take conventional accounting measurement as given rather than, ab initio, seeking to prescribe what we think accounting measurement should be. […] Our attempt has been directed toward approximating conventional accounting by a relatively simple set of axioms and measurement rules, in the same manner that scientists in physics or chemistry have tried to develop a relatively simple set of concepts and theories in order to explain, in satisfactory degrees of approximation, complicated phenomena in this world.

AbstractIn this paper we have applied the mathematical control theory to the accounting network flows, where the flow rates are constrained by linear inequalities. The optimal control policy is of the "generalized bang‐bang" variety which is obtained by solving at each instant in time a linear programming problem whose objective function parameters are determined by the "switching function" which is derived from the Hamiltonian function. The interpretation of the adjoint variables of the control problem and the dual evaluators of the linear programming problem demonstrates an interesting interaction of the cross section phase of the problem, which is characterized by linear programming, and the dynamic phase of the problem, which is characterized by control theory.

In this paper we incorporate a linear demand function to model the price‐volume causal relationship into stochastic cost‐volume‐profit (CVP) analysis. We assume that the objective function is to maximize expected profit; other objective functions are also discussed and compared. A linear stochastic model follows from which probabilistic statements can be easily obtained if the random variables are assumed to be multivariate normal. The basic framework is shown to be a special case of project value maximization where project value is the cash flow of the project discounted for time and risk according to the capital asset pricing model. Moreover, an intertemporal extension that considers inventory is developed. In summary, a new approach to stochastic CVP analysis that incorporates the management decision process in an uncertain environment is developed.