We develop a model where a realization-utility investor (Barberis and Xiong, 2009, 2012; Ingersoll and Jin, 2013) optimally targets her liquid-illiquid wealth ratio at a constant w∗. By saving in the risk-free asset (w∗ 0), she makes smaller bets in the illiquid asset and realizes gains/losses...

We consider a long-term portfolio choice problem with two illiquid and correlated assets and formulate it as an eigenvalue problem in the form of a variational inequality. The eigenvalue is associated with the portfolio’s optimal long-term growth rate, and the free boundaries implied by the...

We study a dynamic mean-variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time-inconsistency involved in a mean-variance criterion, we aim to learn an equilibrium strategy. Under an...

In contrast to traditional financial advising, robo-advising needs to elicit investors’ risk profile via several simple online questions and provide advice consistent with conventional investment wisdom, e.g., rich and young people should invest more in risky assets. To meet the two...