ContinuousTime Portfolio Choice Under Monotone MeanVariance PreferencesStochastic Factor Case
Abstract
We consider an incomplete market with a nontradable stochastic factor and a continuous time investment problem with an optimality criterion based on monotone meanvariance preferences. We formulate it as a stochastic differential game problem and use HamiltonJacobiBellmanIsaacs equations to find an optimal investment strategy and the value function. What is more, we show that our solution is also optimal for the classical Markowitz problem and every optimal solution for the classical Markowitz problem is optimal also for the monotone meanvariance preferences. These results are interesting because the original Markowitz functional is not monotone, and it was observed that in the case of a static oneperiod optimization problem the solutions for those two functionals are different. In addition, we determine explicit Markowitz strategies in the square root factor models.
 Publication:

arXiv eprints
 Pub Date:
 March 2014
 arXiv:
 arXiv:1403.3212
 Bibcode:
 2014arXiv1403.3212T
 Keywords:

 Quantitative Finance  Portfolio Management;
 Mathematics  Probability;
 91G10;
 91A15;
 91A23;
 93E20
 EPrint:
 Major revision, the same model but the main result is strenghtened, the square root factor model added (Heston model)