> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Arrow-Pratt CE Approximation

> Calculate Arrow-Pratt second-order approximation of certainty equivalent: CE ≈ μ - (A/2)*σ² where μ is mean, σ² is variance, and A is absolute risk aversion. Valid for small risks and provides closed-form approximation without numerical inversion. Returns approximate certainty equivalent. Use for quick risk adjustments and mean-variance analysis. [Tier: STANDARD, Credits: 2]



## OpenAPI

````yaml api-specs/economics.json post /quantlib/economics/utility/certainty-equivalent-approximation
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Economics
  description: >-
    Economics module endpoints for FinceptQuantLib API - general equilibrium,
    game theory, auctions, and utility functions
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-economics
    description: >-
      Economics module - general equilibrium, game theory, auctions, and utility
      theory
    x-displayName: Economics
paths:
  /quantlib/economics/utility/certainty-equivalent-approximation:
    post:
      tags:
        - quantlib-economics
      summary: Arrow-Pratt CE Approximation
      description: >-
        Calculate Arrow-Pratt second-order approximation of certainty
        equivalent: CE ≈ μ - (A/2)*σ² where μ is mean, σ² is variance, and A is
        absolute risk aversion. Valid for small risks and provides closed-form
        approximation without numerical inversion. Returns approximate certainty
        equivalent. Use for quick risk adjustments and mean-variance analysis.
        [Tier: STANDARD, Credits: 2]
      operationId: >-
        ce_approx_quantlib_economics_utility_certainty_equivalent_approximation_post
      requestBody:
        content:
          application/json:
            schema:
              type: object
              required:
                - mean
                - variance
                - risk_aversion
              properties:
                mean:
                  type: number
                  description: Expected value of the lottery
                  example: 10000
                variance:
                  type: number
                  description: Variance of the lottery outcomes
                  minimum: 0
                  example: 4000000
                risk_aversion:
                  type: number
                  description: Absolute risk aversion coefficient A
                  example: 0.0001
            example:
              mean: 10000
              variance: 4000000
              risk_aversion: 0.0001
        required: true
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      certainty_equivalent:
                        type: number
                        description: 'Arrow-Pratt approximation of CE: μ - (A/2)*σ²'
                        example: 9800
              example:
                success: true
                data:
                  certainty_equivalent: 9800
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          description: Validation Error
          content:
            application/json:
              schema:
                type: object
                properties:
                  detail:
                    type: array
                    items:
                      type: object
              example:
                detail:
                  - loc:
                      - body
                      - variance
                    msg: ensure this value is greater than or equal to 0
                    type: value_error.number.not_ge
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Basic tier or higher
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````