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Title: Robust portfolio selection with benchmarked objectives
In this paper, we propose and analyze a new approach to finding robust portfolios for asset allocation problems. It differs from the usual worst case approach in that a (dynamic) portfolio is evaluated not only by its performance when there is an adversarial opponent (``nature"), but also by its performance relative to a fully informed benchmark investor who behaves optimally given complete knowledge of the model (i.e. nature's decision). This relative performance approach has several important properties: (i) optimal decisions are less pessimistic than portfolios obtained from the usual worst case approach, (ii) the dynamic problem reduces to a convex static optimization problem under reasonable choices of the benchmark portfolio for important classes of models including ambiguous jump-diffusions, and (iii) this static problem is dual to a Bayesian version of a single period asset allocation problem where the prior on the unknown parameters (for the dual problem) correspond to the Lagrange multipliers in this duality relationship.
