Budgeting effectively for Data Privacy Management Software (DPMS) is a multifaceted challenge that necessitates thorough analysis and strategic planning, given the increasing importance of data privacy in our digitalized business landscape. This article seeks to illuminate the intricate details of this process, based on comprehensive economic theories, privacy laws, and mathematical statistics.

Inarguably, the indispensable starting point in budgeting for DPMS is understanding your business's unique data privacy requirements. These requirements are primarily determined by the nature of the data your business handles, the geographical locations it operates in, and the specific industry regulations it adheres to. For instance, organizations that handle sensitive data like health information or financial transactions will need more robust DPMS compared to those dealing with less sensitive data. Similarly, businesses operating in jurisdictions with stringent data privacy laws, such as the European Union's General Data Protection Regulation (GDPR), require more sophisticated software to ensure compliance.

After identifying your business's data privacy requirements, the next step is to appraise the cost of non-compliance. This appraisal draws heavily from law and economics, specifically regulatory economics, which deals with the economic analysis of regulation. Non-compliance costs include fines and penalties imposed by regulatory bodies, litigation costs, and the potential loss of business due to reputational damage. According to the Ponemon Institute's 2020 Cost of a Data Breach Report, the average total cost of a data breach is $3.86 million, a daunting figure that underscores the importance of investing in robust DPMS.

Subsequent to assessing the potential cost of non-compliance, the next logical step is to conduct a thorough market analysis of available DPMS options. This involves the comparison and contrast of different software vendors in terms of their features, scalability, security, customer support, and pricing models. It’s essential to strike a balance between cost-effectiveness and feature-rich solutions. Leveraging decision theory, a branch of theory that deals with identifying the values, uncertainties, and other issues relevant in a given decision, can aid in making an informed choice.

The pricing models of DPMS providers can be quite diverse, ranging from one-time license fees, subscription-based models to modular pricing based on the specific features you choose. To budget effectively, it’s crucial to understand these pricing models and select the one that best aligns with your business's financial capabilities and data privacy needs. Mathematical statistics can help in modeling these costs over time, taking into account factors like inflation, exchange rate fluctuations, and potential changes in data volume and complexity.

Once the above steps have been executed, the final part of the budgeting process involves incorporating the chosen DPMS's cost into your overall IT budget. This may require adjustments in other areas to accommodate the new expenditure, in line with the principle of budget constraint, an economics concept that posits the trade-off between different goods given limited resources.

In conclusion, budgeting effectively for DPMS is not a one-size-fits-all process. It must be tailored to your organization's unique needs and financial capabilities. It demands an understanding of your business's data privacy requirements, a thorough market analysis of available DPMS options, a deep comprehension of different pricing models, and astute budgetary adjustments. All these steps are underpinned by knowledge drawn from diverse disciplines such as law, economics, decision theory, and mathematical statistics, underscoring the complex but critical nature of the task at hand. Given the increasing prevalence of data breaches and the concomitant rise in regulatory scrutiny, the importance of investing in robust DPMS cannot be overstated.