I think we are eligible. The reasons are as furnished below
http://www.ies.gov.in/myaccount-profile-view.php?memid=339What is pasted above is the profile of an officer currently in IES which is available in the official portal of Indian Economic Service. This officer did his postgraduation in Dairy Economics (MSc Dairy Economics), and still got into IES. While the UPSC website says that A candidate for the Indian Economic
Service must have obtained a post
Graduate Degree in Economics/Applied
Economics/ Business Economics/
Econometrics.
So, if Dairy Economics is an acceptable qualification, MSc Environmental and Actuarial Economics should also be acceptable. But, I am not sure about Applied Quantitative Finance as it does not carry the word 'Economics'.