CRRA - chunhualiao/public-docs GitHub Wiki

  1. Computes Expected Utility
    Calculates the expected Constant Relative Risk Aversion (CRRA) utility of terminal wealth for each simulated path. This utility function quantifies investor satisfaction with wealth, accounting for risk aversion.

    CRRA utility function

    $$ U(W) = \begin{cases} \dfrac{W^{1-\gamma}}{1-\gamma}, & \text{if } \gamma \neq 1\[6pt] \ln W, & \text{if } \gamma = 1 \end{cases} $$

    where

    • ( W ) — terminal wealth
    • ( \gamma ) — coefficient of relative risk aversion

    Example

    Suppose an investor has a terminal wealth of $100 000 and a risk-aversion coefficient ( \gamma = 2 ).

    $$ U(100{,}000) = \frac{100{,}000^{,1-2}}{1-2} = \frac{100{,}000^{-1}}{-1} = \frac{1}{100{,}000} = 0.00001 $$