1. The amount that a risk-averse individual is willing to pay to avoid a risk. Consider an individual with initial wealth W and facing a risky prospect that will lead to a final wealth, W̃, that is random. The risk premium, ρ‎, is defined by

so that it equates the utility of the certain wealth level, W − ρ‎, to the expected utility of the risky wealth level, W̃. If E[W̃] = W then ρ‎ > 0 when the utility function is strictly concave.

2. The additional return that a risky asset must pay over that paid by the risk-free security in order to induce risk-averse investors to purchase it. The risk premium is endogenously determined by the equilibrium in financial markets. For example, in the Capital Asset Pricing Model the risk premium on asset i is given by β‎_i(r̄_m − r_f), where β‎_i is the beta coefficient of asset i, r̄_m is the expected return on the market portfolio, and r_f is the return on the risk-free security.