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Specifying Risk-Aversion through a Utility function. We seek a \valuation formula" for the amount we'd pay that: Increases one-to-one with the Mean of the outcome Decreases as the Variance of the outcome (i.e.. Risk) increases Decreases as our Personal Risk-Aversion increases.
Risk Aversion. This chapter looks at a basic concept behind modeling individual preferences in the face of risk. As with any social science, we of course are fallible and susceptible to second-guessing in our theories. It is nearly impossible to model many natural human tendencies such as “playing a hunch” or “being superstitious.”
Risk aversion plays a central role in finan-cial investment, driving the key trade-off between risk and return in the pricing of financial assets. Risk aversion is relevant in principal–agent models, and is the source of the incentives–insurance trade-off that commonly arises in such models.
We now turn to risk aversion and its measurement and implications. For simplicity work with unidimensional set of outcomes, easiest thought of as money. We assume the existence of a v.N-M expected utility function. u ( x ), which can be used to rank outcomes.
Lecture 04 Risk Prefs & EU (34) • Risk-aversion means that the certainty equivalent is smaller than the expected prize. We conclude that a risk-averse vNM utility function must be concave. Risk-aversion and concavity 1 1
Risk Aversion and Insurance: Introduction. To have a passably usable model of choice, we need to be able to say something about how risk affects choice and well-being. What is risk? We’ll define it is as: — “Uncertainty about possible ‘states of the world,”’ e.g., sick or healthy, war or peace, rain or sun, etc. Why do we need a theory of risk?
Lecture 04: Risk Preferences and Expected Utility Theory. Prof. Markus K. Brunnermeier. State-by-state dominance. Stochastic dominance. vNM expected utility theory. Intuition.
