The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed efficient policy may become inefficient when considering...

Liquidation of large portfolios in practice requires a longer time and smaller relative selling speed than the liquidation of small portfolios. Mean-variance optimal liquidation however results in the same relative selling speed and time horizon for small and large positions. We discuss three...

The study of expected utility maximization in continuous-time stochastic market models dates back to the seminal work of Merton 1969 and has since been central to the area of Mathematical Finance. The associated stochastic optimization problems have been extensively studied. The problem...

The explicit results for the classical Merton optimal investment/consumption problem rely on the use of constant risk aversion parameters and exponential discounting. However, many studies have suggested that individual investors can have different risk aversions over time, and they discount...