Which of the following does NOT require a certificate of authority?

Transacting new insurance policies generally requires a certificate of authority because it involves the actual issuance and management of insurance contracts, which are heavily regulated to ensure consumer protection and financial solvency. Insurance companies must obtain this certificate from the appropriate state regulatory authority to legally operate and ensure that they adhere to state laws and regulations.

In contrast, conducting investigations for claims, liquidating former operations, and settling claims under existing policies do not constitute the creation or issuance of new insurance contracts. These activities are more about managing and resolving existing situations rather than initiating new transactions. Therefore, a certificate of authority is not needed for those actions as they fall under processes that insurers are allowed to conduct without needing to prove their authority to issue new policies.