Distributionally Robust Optimisation
DRO optimises performance under the worst distribution in an ambiguity set, not just under a point estimate.
Classical optimisation uses a single estimated distribution; DRO works against a set of plausible distributions.
Ambiguity sets can be defined via moments, Wasserstein balls, or divergence constraints.
In portfolio problems, DRO tilts allocations away from fragile bets that only work under a narrow distribution.
Distributionally robust optimisation replaces the single “best guess” distribution with a family of nearby distributions. As robustness ϵ grows, probability weight is shifted towards bad scenarios, and the preferred decision can switch to a more conservative one.
With ϵ = 0, all scenarios are equally weighted: nominal expected loss selects the decision with the lowest average cost. As ϵ increases, more probability mass moves into the crash scenario: the purple markers shift up on S6.
Decisions with heavy tails (large loss in S6) are penalised more strongly under the robust distribution. The robust optimum can therefore switch from an aggressive portfolio to a more conservative one, even if its nominal average loss is slightly higher. This is the core DRO effect in portfolio and risk system design.