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\ No newline at end of file diff --git a/Markowitz/STD/RANDOM_SEED_9_NUM_ASSETS_5_MARKOWITZ_POI_STD_LIMIT.mof.json.mof.json b/Markowitz/STD/RANDOM_SEED_9_NUM_ASSETS_5_MARKOWITZ_POI_STD_LIMIT.mof.json.mof.json new file mode 100644 index 0000000000000000000000000000000000000000..048441c156739158dc69f35549075c4571d050be --- /dev/null +++ b/Markowitz/STD/RANDOM_SEED_9_NUM_ASSETS_5_MARKOWITZ_POI_STD_LIMIT.mof.json.mof.json @@ -0,0 +1 @@ +{"name":"MathOptFormat 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\ No newline at end of file diff --git a/Markowitz/STD/markowitz_std.jl b/Markowitz/STD/markowitz_std.jl new file mode 100644 index 0000000000000000000000000000000000000000..2d61789832479f8bfb1ef4a7b049826a4085c42c --- /dev/null +++ b/Markowitz/STD/markowitz_std.jl @@ -0,0 +1,74 @@ +using JuMP +using MathOptInterface +using Ipopt + +using COSMO, LinearAlgebra + +# ================ +# Problem setup +# ================ + +# User-defined number of assets +n = 5 # <-- change this as needed +for n in [5, 10, 20, 50, 100, 200, 500, 1000] + for i in 1:10 + # 1) Create a conic model + model = JuMP.Model(COSMO.Optimizer) + set_silent(model) + + # 2) Parameter: standard deviation limit (σ_max) + @variable(model, σ_max in Parameter(0.04)) # e.g. limit = 0.04 + + # 3) Decision variables: x (portfolio weights) + @variable(model, x[1:n] >= 0) + @constraint(model, sum(x) == 1) + + # 4) Randomly generate covariance & returns + + # Generate a random matrix A + A = rand(n, n) + # Build a PSD matrix by Sigma = A' * A + Sigma = A' * A + + # Optionally scale down the matrix to keep variances in a smaller range + Sigma .*= 0.002 # adjust as needed + + # Random expected returns (e.g., range ~ [0, 0.15]) + mu = 0.05 .+ 0.10 .* rand(n) + + # Perform a Cholesky factorization of Sigma + # (For numerical stability, Sigma is guaranteed PSD) + L = cholesky(Symmetric(Sigma)).L + + # 5) Objective: maximize mu' * x + @objective(model, Max, sum(mu[i] * x[i] for i in 1:n)) + + # 6) Conic constraint for the variance limit: + # || L*x || <= σ_max + # which enforces x' * Sigma * x <= (σ_max)^2 + @variable(model, t >= 0) + @constraint(model, [t; L * x] in SecondOrderCone()) + @constraint(model, t <= σ_max) + + # Solve once for initial σ_max + optimize!(model) + + termination_status(model) == MOI.OPTIMAL || error("Optimization unsuccesful.") + + obj = objective_value(model) + + write_to_file(model, "RANDOM_SEED_$(i)_NUM_ASSETS_$(n)_MARKOWITZ_POI_STD_LIMIT.mof.json.mof.json") + + # Check if the file was written correctly + + model_test = read_from_file("RANDOM_SEED_$(i)_NUM_ASSETS_$(n)_MARKOWITZ_POI_STD_LIMIT.mof.json.mof.json"; use_nlp_block = false) + + set_optimizer(model_test, COSMO.Optimizer) + + JuMP.optimize!(model_test) + + termination_status(model_test) == MOI.OPTIMAL || error("Optimization unsuccesful.") + + objective_value(model_test) ≈ obj || error("Objective values do not match.") + end +end \ No newline at end of file