Problems arising in Finance have become a significant source of new developments in Stochastic Analysis. We discuss some recent case studies, in particular some decomposition and representation theorems which are motivated by problems of hedging derivatives and of intertemporal consumption choice.

The paper provides an axiomatic characterization of dynamic risk measures for multi-period financial positions. For the special case of a terminal cash flow, we require that risk depends on its conditional distribution only. We prove a representation theorem for dynamic risk measures and...

We extend the scope of risk measures for which backtesting models are available by proposing a multinomial backtesting method for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We illustrate the performance of our methods in numerical...