In the context of big data governance, the responsibilities of various stakeholders are delineated as follows:

A. Management's Responsibilities:

Management holds the primary responsibility for establishing and maintaining effective data governance frameworks. This includes ensuring that information storage systems are appropriately defined and that processes for updating critical data elements are clear and well-documented. Such measures are essential to maintain data integrity, availability, and confidentiality. The Institute of Internal Auditors (IIA) emphasizes that management is accountable for the design and implementation of data governance structures, policies, and procedures. These structures should encompass data storage solutions and the mechanisms for updating and managing critical data elements.

The Institute of Internal Auditors

B. External Auditors' Responsibilities:

External auditors are tasked with providing independent assurance on the effectiveness of an organization's financial reporting and related controls. While they may consider the implications of big data on financial reporting, their primary focus is not on the periodic monitoring and maintenance of analytical models. Instead, this responsibility typically falls under management or specialized internal functions. The IIA outlines that external auditors assess the overall control environment but do not directly manage or maintain analytical models.

C. The Board's Responsibilities:

The board of directors provides oversight and strategic direction for the organization's data governance initiatives. However, the implementation of specific controls around data quality dimensions is generally delegated to management. The board ensures that appropriate governance structures are in place and that management is effectively addressing data quality and governance issues. According to the IIA, the board's role is to oversee the data governance framework, ensuring that management has implemented effective controls and processes.

The Institute of Internal Auditors

D. Internal Auditors' Responsibilities:

Internal auditors provide independent assurance on the effectiveness of governance, risk management, and control processes, including those related to data quality and security. While they assess and report on the adequacy of controls over data, the responsibility for ensuring data quality and security rests with management. The IIA states that internal auditors evaluate the effectiveness of data governance practices but do not hold primary responsibility for data quality and security.

The Institute of Internal Auditors

In summary, option A accurately reflects management's responsibility in big data governance, aligning with the IIA's guidelines on data governance roles and responsibilities.