{
  "marginal_1": {
    "name": "S1",
    "size": 18,
    "mean": 1.0,
    "variance": 0.33230452674897104
  },
  "marginal_2": {
    "name": "S2",
    "size": 18,
    "mean": 1.0,
    "variance": 2.07690329218107
  },
  "payoff": {
    "name": "abs_spread",
    "description": "Absolute spread |S2 - S1|",
    "strike": 0.0
  },
  "convex_order": {
    "feasible": true,
    "mean_gap": 0.0,
    "min_call_gap": 0.0,
    "max_call_gap": 0.3750000000000001
  },
  "exact_upper": {
    "value": 1.3100823045267491,
    "marginal_1_error": 2.7755575615628914e-17,
    "marginal_2_error": 2.7755575615628914e-17,
    "martingale_error": 9.71445146547012e-17
  },
  "exact_lower": {
    "value": 0.8753612143294685,
    "marginal_1_error": 2.7755575615628914e-17,
    "marginal_2_error": 6.938893903907228e-17,
    "martingale_error": 1.9949319973733282e-17
  },
  "benchmarks": {
    "unrestricted_min_comonotone": 0.7500000000187503,
    "independent": 1.3166666679515544,
    "unrestricted_max_countermonotone": 1.7500000000437506
  },
  "regularized": {
    "0.15": {
      "expected_payoff": 1.2486501512385084,
      "regularized_primal": 1.3356488212811268,
      "dual_value": 1.3356487918208306,
      "dual_gap": -2.9460296202543645e-08,
      "converged": true,
      "iterations": 38,
      "marginal_1_error": 9.934152320201228e-10,
      "marginal_2_error": 9.020562075079397e-17,
      "martingale_error": 6.730012366840121e-09
    },
    "0.4": {
      "expected_payoff": 1.1898829099182027,
      "regularized_primal": 1.5212307785357175,
      "dual_value": 1.5212307541984198,
      "dual_gap": -2.4337297732657248e-08,
      "converged": true,
      "iterations": 18,
      "marginal_1_error": 6.109282316146825e-10,
      "marginal_2_error": 4.85722573273506e-17,
      "martingale_error": 4.895687980011054e-09
    }
  }
}