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This paper considers a robust time-consistent mean-variance-skewnessportfolio selection problem for an ambiguity-averse investor by taking intoaccount wealth-dependent risk aversion and wealth-dependent skewness preferenceas well as model uncertainty. The robust equilibrium investment strategy andcorresponding equilibrium value function are characterized for such a problemby employing an extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) system via agame theoretic approach. Furthermore, the robust equilibrium investmentstrategy and corresponding equilibrium value function are obtained insemi-closed form for a special robust time-consistent mean-variance-skewnessportfolio selection problem. Finally, some numerical experiments are providedto indicate several new findings concerned with the robust equilibriuminvestment strategy and the utility losses.

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem