I am a Pure Maths PhD student researching in functional analysis, particularly Banach space theory,
Recently I came across stochastic control theory, which perform optimization using stochastic (uncertainty). ] I am fascinated by the use Stochastic calculus on optimization, which I would never think about it if I never come across it.
I am interested to know how many fields would require stochastic knowledge.
Some fields that I know are Stochastic programming, mathematical finance (Black-Scholes equation).