options_pricing.jl

# Section 4.4 of
# A. A. Ahmadi, and A. Majumdar
# DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
# 2017

using MultivariateMoments

@testset "Options Pricing with $(factory.constructor)" for factory in sdp_factories
    iscsdp(factory) && continue
    isscs(factory) && continue
    VERSION < v"1.0.3" && continue # see https://github.com/JuliaOpt/SumOfSquares.jl/issues/48
    @polyvar x y z
    σ = [184.04, 164.88, 164.88, 184.04, 164.88, 184.04]
    X = [x^2, x*y, x*z, y^2, y*z, z^2, x, y, z, 1]
    μ = measure([σ .+ 44.21^2; 44.21 * ones(3); 1],
                X)

    dsos_codsos_exp   = [132.63, 132.63, 132.63, 132.63, 132.63]
    sdsos_cosdsos_exp = [ 21.51,  17.17,  13.20,   9.85,   7.30]
    sos_cosos_exp = sdsos_cosdsos_exp
    @testset "with $cone" for (cone, exp) in [(CopositiveInner(DSOSCone()), dsos_codsos_exp),
                                              (CopositiveInner(SDSOSCone()), sdsos_cosdsos_exp),
                                              (CopositiveInner(SOSCone()), sdsos_cosdsos_exp)]
        function optionspricing(K, cone)
            m = SOSModel(factory)
            @variable m p Poly(X)
            @constraint m p in cone
            @constraint m p - (x - K) in cone
            @constraint m p - (y - K) in cone
            @constraint m p - (z - K) in cone
            @objective m Min dot(μ, p)
            JuMP.optimize!(m)
            @test JuMP.primal_status(m) == MOI.FEASIBLE_POINT
            JuMP.objective_value(m)
        end

        K = [30, 35, 40, 45, 50]
        for i in eachindex(K)
            @test optionspricing(K[i], cone) ≈ exp[i] atol=1e-2
        end
    end
end