We propose a linear bi-objective optimization approach to the problem of finding a portfolio that maximizes average excess return with respect to a benchmark index while minimizing underperformance over a learning period. We establish some theoretical results linking classical No Arbitrage...

Enhanced Indexation is the problem of selecting a portfolio that should produce excess return with respect to a given benchmark index. In this work we propose a linear bi-objective optimization approach to Enhanced Indexation that maximizes average excess return and minimizes underperformance...

Enhanced Index Tracking is the problem of selecting a portfolio that should generate excess return with respect to a benchmark index. Here we propose a large-size linear optimization model for Enhanced Index Tracking that selects an optimal portfolio according to a new stochastic dominance...

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the...

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the...

We solve two related extremal problems in the theory of permutations. A set Q of permutations of the integers 1 to n is inversion-complete (resp., pair-complete) if for every inversion (j, i), where 1 <= i < j <= n, (resp., for every pair (i, j), where i not= j) there exists a permutation in Q where j is before i. It is minimally inversion-complete if in addition no proper subset of Q is inversion-complete; and similarly for paircompleteness. The problems we consider are to determine the maximum cardinality of a minimal inversion-complete set of permutations, and that of a minimal pair-complete set of permutations. The latter problem arises in the determination of the Carathéodory numbers for certain abstract convexity structures on the (n - 1)-dimensional real and integer vector spaces. Using Mantel's Theorem on the maximum number of edges in a triangle-free graph, we determine these two maximum cardinalities and we present a complete description of the optimal sets of permutations for each problem. Perhaps surprisingly (since there are twice as many pairs to cover as inversions), these two maximum cardinalities coincide whenever n >= 4.