  This paper enhances the pricing of derivatives as well as optimal control
problems to a level comprising risk. We employ nested risk measures to quantify
risk, investigate the limiting behavior of nested risk measures within the
classical models in finance and characterize existence of the risk-averse
limit. As a result we demonstrate that the nested limit is unique, irrespective
of the initially chosen risk measure. Within the classical models risk aversion
gives rise to a stream of risk premiums, comparable to dividend payments. In
this context we connect coherent risk measures with the Sharpe ratio from
modern portfolio theory and extract the Z-spread -- a widely accepted quantity
in economics to hedge risk. The results for European option pricing are then
extended to risk-averse American options, where we study the impact of risk on
the price as well as the optimal time to exercise the option. We also extend
Merton's optimal consumption problem to the risk-averse setting.
