A choice may not have a certain outcome.
For example an action could have have 50
We can model any risk preference as:
If the agent is risk neutral we can use:
If the agent is risk averse:
If the agent is risk loving we can use:
Given a utility function we can calculate the risk aversion.
Constant Absolute Risk Aversion (CARA) is:
Hyperbolic Absolute Risk Aversion (HARA) is:
Increasing and Decreasing Absolute Risk Aversion (IARA and DARA):
Risk aversion increase or decreases in \(x\).
Absolute risk aversion is:
If an agent faces an uncertain world they can make decisions under uncertainty. For example, how would an agent value £10 relative to a 50 There are many different attitudes an agent could have – we need a form which can capture these. A standard approach is expected utility.
We start by taking
Subjective expected utility
HARA Hyperbolic Absolute Risk Aversion
CRRA Constant Relative Risk Aversion
Cumulative prospect theory.