Mean-Expectile Portfolio Selection

We consider a mean-expectile portfolio selection problem in a continuous-time diffusion model. We exploit the close relationship between expectiles and the Omega performance measure to reformulate the problem as the maximization of the Omega measure, and show the equivalence between the two problems. After showing that the solution for the mean-expectile problem is not attainable but that the value function is finite, we modify the problem by introducing a bound on terminal wealth and obtain the solution by Lagrangian duality. The global expectile minimizing portfolio and efficient frontier with a terminal wealth bound are also discussed.