  Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly
popular in financial applications, owing to certain desirable properties that
it enjoys. We consider the problem of estimating UBSR in a recursive setting,
where samples from the underlying loss distribution are available
one-at-a-time. We cast the UBSR estimation problem as a root finding problem,
and propose stochastic approximation-based estimations schemes. We derive
non-asymptotic bounds on the estimation error in the number of samples. We also
consider the problem of UBSR optimization within a parameterized class of
random variables. We propose a stochastic gradient descent based algorithm for
UBSR optimization, and derive non-asymptotic bounds on its convergence.
