Quantification of risk in classical models of finance

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