<p>This study examines the impact of integrating green assets into multi-asset portfolios for three investor profiles: risk-averse, neutral, and risk-taking. Using multi-objective optimization (MOO), we construct and compare portfolios with and without green assets, then evaluate their relative performance using stochastic dominance up to the third order. The results reveal that the addition of green assets, particularly green bonds and green electricity, significantly transforms allocations for risk-averse and neutral profiles. Green bonds, thanks to their low volatility, become a pillar of conservative portfolios, while green electricity plays a complementary role in diversification. Stochastic dominance tests show that, in the second and third orders, portfolios incorporating green assets systematically outperform their equivalents without green assets for both profiles. On the other hand, for risk-taking investors, the weighting remains largely concentrated on highly volatile equities (mainly the DAX index), making the presence of green assets marginal and removing any link of dominance. These results highlight the strategic value of green assets as instruments of stability and diversification within prudent, balanced strategies, while underscoring their limited appeal to strategies focused purely on gross performance.</p>