Now in universities there are quite a few programs that combine the basics of informatics and economics, for example, Applied Informatics in Economics, Information Security of Financial and Economic Structures, Mathematical and Information Support of Economic Activity, etc. Here, see the full list, study the content training programs.
Yes, there is a lot of this in the entire spectrum from "almost completely programming" to "almost completely economics". More programming is enterprise management systems. Of the specific products, this is primarily 1C and SAP programming, but there are also many self-made and smaller \ specialized production management systems (and there are a lot of databases, SQL, etc.). You need to know how to program them and understand why and how this system will work in the future. There you need to learn programming and have skills in a specific language (there are many programs with certificates).
Most of the applied econometrics for business (demand estimation, etc.) is now almost mandatory programming, click the button in the statistical package is no longer enough. This is doubly true for financiers, especially "quanta". Often it is enough just to be able to write working code (Sheppard Python for Econometrics), but knowledge of econometrics for this must be very serious.
In research, this is primarily algorithmic game theory, which with the question "what are the equilibria of the auction" moves on to the question "is it possible to calculate such an auction at all?" Recently, computer security is also being considered from the economic side. On a similar cryptographic note, blockchains and all the hype around Bitcoin (and all startups tied to them) require both an understanding of cryptography and an understanding of the economy (the same currency risks).