Explanation:

- Sri Aurobindo was a prominent freedom fighter and philosopher. However, he did not write a thesis titled 'The Problem of Rupee'.

- Dr. Rajendra Prasad was the first President of India and a lawyer by profession. He didn't author this thesis.

- Pt. Jawaharlal Nehru was India's first Prime Minister, well-known for his books on Indian history and politics, but not for this specific thesis.

- Dr. Bhimrao Ambedkar was an economist, jurist, and the principal architect of the Indian Constitution. He wrote his doctoral thesis on 'The Problem of the Rupee: Its Origin and Its Solution'.

The correct answer is:

- Option 4 Dr. Bhimrao Ambedkar