Which framework provides industry-wide guidance for securely developing applications?

The correct answer is ISO/IEC 27034. This framework specifically focuses on providing guidance for the management of security in applications and allows organizations to develop software in a secure manner. ISO/IEC 27034 includes best practices and standards necessary for integrating security into the application lifecycle, addressing various stages from requirement gathering to deployment and maintenance.

While the other options do provide useful security frameworks and guidelines, they serve different purposes. The Open Web Application Security Project (OWASP) is well-known for its emphasis on securing web applications and offers essential resources, but it does not serve as a comprehensive framework like ISO/IEC 27034. Build Security In (BSI) emphasizes the integration of security into the software development lifecycle but is more of a philosophy than a formalized framework. API Management refers to the strategies and tools for handling APIs but does not primarily address application security development comprehensively. Hence, ISO/IEC 27034 stands out for its specific focus on secure application development across industries.