Optimal smoothing of accounting earnings

Accountants seeking to estimate the profitability of a firmvia the calculation of earnings utilize information about thenumber and current lifespan of unfinished activities by incorporatinga smoothing device—depreciation—into their calculations.This paper considers a firm in steady state, carrying out alarge number of similar activities with random starts and completiondates. By developing a stochastic model for the firm's activities,a difference equation for the minimum-variance smoothing functionis obtained. This can be solved explicitly in the case of aperiodic Poisson process of start times and independent exponentialdurations and is a variant of declining-balance depreciation.     

Long-time behaviour of solutions of an electrophoretic model with a single reaction

A electrochemical model consisting of three charged speciesis considered. The ions diffuse owing to concentration gradientsand migrate because of electric force. Reversible reaction isallowed to take place between these species. It is shown that,provided the total of initial charges in the electrolyte iszero, any initial distribution of species concentrations willconverge to a unique steady state as time becomes large.     

The statistical analysis of standard-cost deviations

Very little is known about the theoretical statistical propertiesof accounting numbers. In this papera probability modellingtechnique is used to analyse the volume, efficiency, and pricedeviation—more usually known in the accounting literatureas ‘variances’—of standard costing. Standard-costdeviations are defined asdifferences between certain types ofconditional and unconditional expected costs. The basic statisticsrequired to construct theoretical confidence intervals for thesedifferences are identified, and it is shown how the formulaenormally used in their calculation may sometimes be correlated.The modelling technique adopted is based on a theory of accountingmeasurement which interprets accounting numbers as specializedtypes of statistics. It illustrates the potential of the theoryfor the development of a better understanding of the statisticalproperties of accounting numbers.     

Bayesian decision-making in inventory modelling

The objective of this paper is to advocate the use of Bayesianmethods in tackling decision problems with limited past data.It is assumed that a Bayesian approach is least likely to besuccessful when there is no information on which to base a meaningfulprior. Here we use a limiting, invariant, form of the conjugateprior distribution to represent this ignorance. The resultsof decisions based on Bayesian methods with this ‘non-informative’prior are compared with those which result from deriving a pointestimate for the unknown parameter. The particular context consideredhere is that of a single-period inventory model with compoundPoisson demand made up of a known demand size distribution butan unknown demand rate. The demand rate is assumed to be highenough for a normal approximation to the compound Poisson distributionto be used, in which case it is possible to analyse the behaviourdirectly. An extension to the multi-period model with zero leadtime is considered briefly. The results lend support to theuse of Bayesian methods, with or without a meaningful prior,for which the analysis and computation are no more complex thanthose required by standard methods.     

Extension of the Virasoro and Neveu-Schwarz Algebras and Generalized Sturm-Liouville Operators

We consider the universal central extension of the Lie algebra Vect(S ¹) C(S ¹). The coadjoint representation of thisLie algebra has a natural geometric interpretation by matrix analogues ofthe Sturm –Liouville operators. This approach leads to new Liesuperalgebras generalizing the well-known Neveu –Schwarz algebra.