Build a rigorous understanding of how preferences, utility functions, and risk aversion power modern financial mathematics, from deterministic choice to uncertainty and portfolio optimization.
Progress through a structured learning path that connects preference theory with financial practice.
Review deterministic preference axioms and ordinal utility
Extend to uncertainty with expected utility theory
Quantify investor risk attitudes using Arrow–Pratt metrics
Apply utility optimization to portfolio and market models
Use expected utility maximization to derive optimal asset allocations across risky and risk-free securities.
Connect utility curvature with mean-variance optimization and stochastic dominance rules.
Quantify risk premiums demanded by risk-averse investors using Arrow–Pratt measures.
Assess certainty equivalents and insurance pricing under different utility specifications.
Identify limitations of expected utility theory and motivate advanced models like prospect theory.
Explore empirical anomalies, including Allais and Ellsberg paradoxes, that shape modern behavioral finance.
The certainty equivalent translates an uncertain payoff X into a guaranteed amount that delivers identical utility:
This expression underpins insurance pricing and portfolio optimization decisions.
Ordinal utility admits any strictly increasing transformation without altering preference rankings:
The property explains why utility maximization remains consistent after monotonic rescaling.
Utility theory provides the microeconomic foundation for portfolio choice, asset pricing, and risk management. It enables investors to rank uncertain outcomes, quantify trade-offs between risk and return, and derive optimal strategies consistent with rational preference axioms.
Deterministic models assume outcomes are known with certainty and focus on ordinal preference representation. Stochastic models incorporate probability distributions over outcomes, leading to expected utility frameworks that weight payoffs by both magnitude and likelihood.
Arrow–Pratt absolute and relative risk aversion measures quantify the curvature of utility functions. They help practitioners calibrate risk premiums, design insurance products, and tailor investment strategies to investor risk tolerance.