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 [2] based on the recognition that avoiding loss of a significant magnitude is a matter of great concern to most investors.

[37], and Wu and Chen [38] consider the investment model with regime switching under a mean-variance criterion. Cheung and Yang [39], 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.

Mean-variance criterion pioneered by Markowitz [2] 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 problem.

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.

[8] 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 [2].

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.