For those interested in microeconomics, the Medallion Fund is probably the most profitable application of Markov chains to date (also the most profitable mutual fund to date). It was founded by renowned mathematician Jim Simons [0], building upon the Baum–Welch algorithm [1]. Very interesting stuff.
Could you elaborate on how exactly a Markov chain used there. Baum Welch is for HMMs though, which are different from Markov chains, they can capture infinite history/memory.