Explanation:

- Amartya Sen, an Indian economist and philosopher, is renowned for his work in welfare economics, social choice theory, and economic justice.

- Option 1: 1998 - Amartya Sen was awarded the Nobel Prize in Economics for his contributions to welfare economics, particularly his research on famine, human development theory, and the capabilities approach.

- Option 2: 2004 - This year is incorrect as Amartya Sen did not receive the Nobel Prize in this year.

- Option 3: 1997 - In this year, Robert C. Merton and Myron S. Scholes were awarded the prize for a new method to determine the value of derivatives.

- Option 4: 1999 - This is incorrect, as the Nobel was awarded to Robert A. Mundell for his analysis of monetary and fiscal policy under different exchange rate regimes.