MATHEMATICAL MODEL OF PRICING OF PERSONAL MILITARY ACCOUNTING AUDIT AT ENTERPRISES

Abstract

Introduction. Under martial law, personnel military registration at enterprises has become an essential component of the system of economic security, workforce resilience, and business continuity. The growing number of regulatory requirements, the increasing liability of enterprise managers, and the rising cost of potential losses necessitate a transition from traditional cost-based approaches to audit pricing toward risk-oriented pricing models that adequately reflect the actual level of managerial risk.

Purpose. To provide a theoretical and methodological foundation for, and to develop, a mathematical pricing model for the audit of personnel military registration at enterprises based on the assessment of aggregate managerial risk.

Materials and Methods. The study employed systemic, structural-functional, logical, economic-mathematical, comparative, and risk-oriented approaches. The research methodology included scientific abstraction, analysis and synthesis, mathematical modelling, functional analysis, risk aggregation, comparative analysis of mathematical pricing models, and graphical modelling for the visualization of research findings.

Results. For the first time, a mathematical pricing model for the audit of personnel military registration at enterprises has been developed, in which the audit fee is determined as a function of aggregate managerial risk. The structure of aggregate risk has been formalized through the aggregation of local risks defined by the probability of an adverse event, the magnitude of its impact, and the severity of its consequences. Based on a comparative analysis of mathematical pricing models, the suitability of the Cobb–Douglas multiplicative function has been substantiated due to its monotonicity, scalability, economic interpretability of parameters, and the possibility of logarithmic transformation for subsequent statistical calibration. It has been demonstrated that the economic value of an audit of personnel military registration is determined not by the labour intensity of audit procedures but by its ability to reduce the enterprise's aggregate managerial risk. The proposed model establishes a theoretical foundation for the transition to risk-oriented pricing of audit services and may serve as the basis for developing digital audit pricing calculators, automated decision-support systems, and methodologies for the economic justification of specialized audit service fees. The scientific novelty of the study lies in the development of a new risk-oriented approach to pricing the audit of personnel military registration, which, unlike traditional cost-based, hourly, and linear pricing models, is based on the quantitative assessment of aggregate managerial risk using a multiplicative mathematical function. The proposed model may be applied by consulting companies, internal auditors, enterprise economic security units, audit firms, and developers of digital information systems to establish a transparent, economically justified mechanism for determining the price of personnel military registration audits.

Prospects. Future research should focus on the empirical validation of the proposed model, statistical estimation of its parameters, the development of industry-specific methodologies for determining risk coefficients, the creation of digital audit pricing calculators, and the integration of the proposed model into enterprise economic security management systems.