riskaversion

Risk aversion is a tendency to prefer a certain outcome over a gamble with the same expected value. A risk-averse person will accept a certain payoff CE that is smaller than the gamble’s expected value EV, and the difference EV − CE is the risk premium required to bear risk.

In expected utility theory, risk aversion arises from a concave utility of wealth: as wealth increases, marginal utility declines, making uncertainties costly. The degree of risk aversion is summarized by the Arrow-Pratt measures: absolute risk aversion A(x) = −u''(x)/u'(x) and relative risk aversion R(x) = −x u''(x)/u'(x). Higher values indicate stronger aversion.

In finance and economics, risk aversion helps explain asset pricing and portfolio choice. Risk-averse investors require higher expected returns for taking on risk, reducing demand for risky assets and increasing demand for risk-free assets. Insurance products, derivatives, and diversification strategies are designed to manage or transfer risk in line with risk preferences.

Factors influencing risk aversion include wealth level, time horizon, health, income stability, information, and context or domain. Risk attitudes can vary across individuals and situations and may change with framing, experience, or market conditions. Prospect theory notes that loss framing and probability weighting can alter apparent risk preferences, especially for gains versus losses.

Limitations: risk aversion is not fixed and can be domain-specific; measures often assume rational, consistent preferences, which may fail in practice. Nonetheless, the concept remains central to theories of choice under uncertainty and to practical decision making in finance, insurance, and public policy.