Portfolio optimization under downside risk while preserving the upside is of crucial importance to asset managers. In the Black-Scholes setting, we consider one such particular measure given by the notion of capital-at-risk. This paper generalizes the work of Emmer et al., 2001, to the case of time dependent parameters and investment strategies, i.e., continuous-time portfolio optimization, and...

We consider some further applications of martingale pricing to problems in financial engineering. In particular, we will show how dynamic portfolio optimization problems in complete markets may be solved using martingale pricing methods. We will see, as a result, how the problems of security pricing and portfolio optimization are very closely related. We then introduce real options and discuss ...