In addition to the mean-variance criterion, there is another important school of thought called the safety-first criterion, which can be traced back to the work by Roy  based on the recognition that avoiding loss of a significant magnitude is a matter of great concern to most investors.
, and Wu and Chen  consider the investment model with regime switching under a mean-variance criterion. Cheung and Yang , Zeng et al.
Therefore, the maximization of the mean-variance criterion
is used in practice:
But it is well known that this mean-variance criterion
lacks of iterated-expectation property, which gives rise to time-inconsistent investment strategy in the sense that Bellman optimality principle is not available any more.
If we compare the first two moments (mean-variance analysis), note that for m high, the expectation and variance of the CPPI portfolio are greater than those of the OBPI one and so there is no-dominance with respect to the mean-variance criterion
. For any parametrization of the financial markets, there exists at least one value for m such that the OBPI strategy dominates, in a mean-variance sense, the CPPI one.
If the decision-maker is risk-averse or if the outcome distributions are normally distributed, then the familiar mean-variance criterion
can be used to select the optimal hedging strategy.
pioneered by Markowitz  has been one of the key research topics in financial economics and has stimulated numerous extensions and applications from different perspectives.
When C = 0, (1) becomes a mean-variance criterion
Equilibrium time-consistent strategy for corporate international investment problem with mean-variance criterion
is proposed and founded in "Equilibrium Time-Consistent Strategy for Corporate International Investment Problem with Mean-Variance Criterion
" by J.
 apply the Heston's SV model to investigate the reinsurance and investment problem under the mean-variance criterion
We assume two experts that have different beliefs on the fundamental of an asset and choose their allocations by using the mean-variance criterion
in every moment in time .
In this paper, we are concerned with optimal investment strategy for the dual risk model under mean-variance criterion
. Our objective is to find the optimal investment strategy such that the expected terminal wealth is maximized and the variance of the terminal wealth is minimized.