> ## 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.

# Quadratic Utility Function

> Evaluate quadratic utility function: U(w) = a*w - b*w^2 where a, b > 0. Returns utility value, marginal utility (a - 2*b*w), absolute risk aversion (2b/(a-2bw)), and satiation point (a/2b where marginal utility = 0). Quadratic utility exhibits increasing absolute risk aversion (IARA). Has a bliss point beyond which more wealth decreases utility. Use for mean-variance analysis and portfolio theory. [Tier: STANDARD, Credits: 2]



## OpenAPI

````yaml api-specs/economics.json post /quantlib/economics/utility/quadratic
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/quadratic:
    post:
      tags:
        - quantlib-economics
      summary: Quadratic Utility Function
      description: >-
        Evaluate quadratic utility function: U(w) = a*w - b*w^2 where a, b > 0.
        Returns utility value, marginal utility (a - 2*b*w), absolute risk
        aversion (2b/(a-2bw)), and satiation point (a/2b where marginal utility
        = 0). Quadratic utility exhibits increasing absolute risk aversion
        (IARA). Has a bliss point beyond which more wealth decreases utility.
        Use for mean-variance analysis and portfolio theory. [Tier: STANDARD,
        Credits: 2]
      operationId: quadratic_utility_quantlib_economics_utility_quadratic_post
      requestBody:
        content:
          application/json:
            schema:
              type: object
              required:
                - a
                - b
                - wealth
              properties:
                a:
                  type: number
                  description: Linear coefficient (a > 0)
                  minimum: 0
                  exclusiveMinimum: true
                  example: 1
                b:
                  type: number
                  description: Quadratic coefficient (b > 0)
                  minimum: 0
                  exclusiveMinimum: true
                  example: 0.0001
                wealth:
                  type: number
                  description: Current wealth level
                  example: 1000
            example:
              a: 1
              b: 0.0001
              wealth: 1000
        required: true
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      utility:
                        type: number
                        description: Utility value at given wealth
                        example: 900
                      marginal_utility:
                        type: number
                        description: First derivative U'(w) = a - 2*b*w
                        example: 0.8
                      absolute_risk_aversion:
                        type: number
                        description: Absolute risk aversion -U''(w)/U'(w) = 2b/(a-2bw)
                        example: 0.00025
                      satiation_point:
                        type: number
                        description: >-
                          Wealth level where marginal utility becomes zero
                          (a/2b)
                        example: 5000
              example:
                success: true
                data:
                  utility: 900
                  marginal_utility: 0.8
                  absolute_risk_aversion: 0.00025
                  satiation_point: 5000
        '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
                      - a
                    msg: field required
                    type: value_error.missing
      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

````