This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a...

We consider portfolio optimization problems with expected loss constraints under the physical measure P and the risk neutral measure Q, respectively. Using Merton's portfolio as a benchmark portfolio, the optimal terminal wealth of the Q-risk constraint problem can be easily replicated with the...