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Abstract
ABSTRACTIn expected utility theory, aversion to risk, greater aversion, and the desire to substitute away from risk are each characterized by properties of the Arrow–Pratt index of absolute risk aversion, with comparative statics implications for such decisions as saving. At the third order, however, no single index suffices. We contrast alternative indices of third‐order risk preference and show that the substitution effect of downside risk is governed by the Schwarzian, and that where the degree of prudence governs the magnitude of precautionary saving, the Schwarzian governs the effect of background risk on the marginal rate of time preference.
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