action portfoliooptimizer_post_portfolio_optimization_mean_variance_efficient_subset_resam {
  label: "Subset Resampling-Based Mean-Variance Efficient Portfolio"
  description: "Compute the asset weights of a subset resampling-based  mean-variance efficient portfolio, following the methodology described in the first and the second references, optionally subject to:  \n* Minimum and maximum weights constraints\n* Maximum group weights constraints\n* Minimum and maximum portfolio exposure constraints\n\nReferences\n * [CSSA, Random Subspace Optimization (RSO)](https://cssanalytics.wordpress.com/2013/10/06/random-subspace-optimization-rso/)\n * [Subset Optimization for Asset Allocation,Benjamin J. Gillen](https://www.bengillen.com/uploads/1/2/3/8/123891022/subsets.pdf)\n * Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments, Second edition, Blackwell Publishers Inc.\n"
  provider: portfoliooptimizer
  method: POST
  path: "/portfolio/optimization/mean-variance-efficient/subset-resampling-based"
  encoding: json
  input: {
    type: "object"
    required: ["assets", "assetsCovarianceMatrix", "assetsReturns", "constraints"]
    properties: {
      assets: {
        type: "integer"
        description: "The number of assets"
      }
      assetsCovarianceMatrix: {
        type: "array"
        description: "assetsCovarianceMatrix[i][j] is the covariance between the asset i and the asset j"
        items: {
          type: "array"
          items: {
            type: "number"
          }
        }
      }
      assetsReturns: {
        type: "array"
        description: "assetsReturns[i] is the arithmetic return of asset i"
        items: {
          type: "number"
        }
      }
      constraints: {
        type: "object"
        properties: {
          assetsGroups: {
            type: "array"
            items: {
              type: "array"
              description: "assetsGroups[k] is the indexes of the assets belonging to the assets group k in the portfolio; exclusive with assetsGroupsMatrix"
              items: {
                type: "integer"
              }
            }
          }
          assetsGroupsMatrix: {
            type: "array"
            description: "assetsGroupsMatrix[k][i] is the weight of the asset i in the group of assets k; exclusive with assetsGroups"
            items: {
              type: "array"
              items: {
                type: "number"
              }
            }
          }
          maximumAssetsGroupsWeights: {
            type: "array"
            description: "maximumAssetsGroupsWeights[k] is the maximum weight of the assets group k in the portfolio, in percentage between 0 and 1 if assetsGroups is provided"
            items: {
              type: "number"
            }
          }
          maximumAssetsWeights: {
            type: "array"
            description: "maximumAssetsWeights[i] is the maximum weight of the asset i in the portfolio, in percentage"
            items: {
              type: "number"
            }
          }
          maximumPortfolioExposure: {
            type: "number"
            description: "The maximum portfolio exposure; must be higher than or equal to minimumPortfolioExposure"
          }
          minimumAssetsWeights: {
            type: "array"
            description: "minimumAssetsWeights[i] is the minimum weight of the asset i in the portfolio, in percentage"
            items: {
              type: "number"
            }
          }
          minimumPortfolioExposure: {
            type: "number"
            description: "The minimum portfolio exposure; must be lower than or equal to maximumPortfolioExposure"
          }
          portfolioReturn: {
            type: "number"
            description: "The portfolio return; exclusive with portfolioVolatility and riskTolerance"
          }
          portfolioVolatility: {
            type: "number"
            description: "The portfolio volatility; exclusive with portfolioReturn and riskTolerance"
          }
          riskTolerance: {
            type: "number"
            description: "The portfolio risk tolerance; exclusive with portfolioReturn and portfolioVolatility"
          }
        }
      }
      subsetPortfolios: {
        type: "integer"
        description: "The number of subset portfolios to compute; only applicable if the enumeration method for the subset portfolios is random sampling"
      }
      subsetPortfoliosAggregationMethod: {
        type: "string"
        description: "The method to aggregate the subset portfolios"
        enum: ["average", "median"]
      }
      subsetPortfoliosEnumerationMethod: {
        type: "string"
        description: "The method to enumerate the subset portfolios"
        enum: ["complete", "randomSampling"]
      }
      subsetSize: {
        type: "integer"
        description: "The number of assets to include in each subset portfolio; defaults to a value of order the square root of the total number of assets"
      }
    }
  }
  output: {
    type: "object"
    required: ["assetsWeights"]
    properties: {
      assetsWeights: {
        type: "array"
        description: "assetsWeights[i] is the weight of the asset i in the portfolio, in percentage"
        items: {
          type: "number"
        }
      }
    }
  }
}