Certainty equivalent API

Computes expected utility, certainty equivalent and risk premium for a gamble under exponential (CARA), log, or power (CRRA) utility, classifying the risk attitude. Answers 'What guaranteed amount equals this risky bet for a risk-averse agent?', 'What is the risk premium under CARA utility?'.

Price$0.08per request

MethodPOST

Route/v1/gametheory/certainty-equivalent

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

decision-theoryexpected-utilitycertainty-equivalentrisk-aversioncaracrrarisk-premiumeconomics

API URLhttps://x402.hexl.dev/v1/gametheory/certainty-equivalent

Integration docs

Example request

{
  "values": [
    0,
    100
  ],
  "probabilities": [
    0.5,
    0.5
  ],
  "riskAversion": 0.01,
  "utility": "exponential"
}

Example response

{
  "utility": "exponential",
  "riskAversion": 0.01,
  "expectedValue": 50,
  "expectedUtility": 0.68393972,
  "certaintyEquivalent": 37.988549,
  "riskPremium": 12.011451,
  "attitude": "risk-averse",
  "interpretation": "A risk-averse agent values this gamble at a certainty equivalent of 37.99 vs. expected value 50 (risk premium 12.01)."
}

Input schema

{
  "type": "object",
  "required": [
    "values",
    "probabilities"
  ],
  "properties": {
    "values": {
      "type": "array",
      "items": {
        "type": "number"
      },
      "examples": [
        [
          0,
          100
        ]
      ]
    },
    "probabilities": {
      "type": "array",
      "items": {
        "type": "number"
      },
      "examples": [
        [
          0.5,
          0.5
        ]
      ]
    },
    "riskAversion": {
      "type": "number",
      "examples": [
        0.01
      ]
    },
    "utility": {
      "type": "string",
      "enum": [
        "exponential",
        "log",
        "power"
      ],
      "examples": [
        "exponential"
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}