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## Axiomatic foundations of multiplier preferences (2007)

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Citations: | 31 - 3 self |

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Citation Context ...sentations of the same preference on B0(Σ, U). By uniqueness, φ(x + k) = α(k)φ(x) + β(k) for all k, x ∈ U. This is a generalization of Pexider’s equation (see equation (3) of Section 3.1.3, p. 148 of =-=Aczél, 1966-=-). If U ∈ {R, R+}, then by Corollary 1 in Section 3.1.3 of Aczél (1966), up to positive affine transformations, the only strictly increasing concave solutions are of the form φθ, for θ ∈ (0, ∞]. It is... |

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Citation Context ...However, the following theorem shows that such caution is equivalent to increased risk aversion. 3.2 Link to Increased Risk Aversion The following variational formula (see, e.g., Proposition 1.4.2 of =-=Dupuis and Ellis, 1997-=-) plays a critical role in the analysis and applications of multiplier preferences. ∫ ( ∫ ( min (u ◦ f) dp + θR(p‖q) = −θ log exp − p∈∆S S S ) ) u ◦ f dq . (7) θ This formula links model uncertainty, ... |

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Citation Context ...ead act and z ∈ Z be a deterministic payoff. Define (1; z, h+1) to be a temporal act where the 24This failure of inference is known in econometrics as the problem of incidental parameters (see, e.g., =-=Neyman and Scott, 1948-=-). 30subjective uncertainty about h+1 is resolved in period 1, i.e., whose chance node for period 0 is degenerate. Formally, define (1; z, h+1)(s) = (z, h+1) for all s ∈ S. On the other hand, define ... |

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Citation Context ...The other approach is to keep q but to introduce another parameter that captures the higher aversion toward variability coming from one source than another, as in the SOEU model (Neilson, 1993, 2009; =-=Nau, 2001-=-, 2006; Ergin and Gul, 2009; Grant et al., 2009). As this paper shows (see Section 3.3), the multiplier preferences have both representations and for this reason they belong to both families of models... |

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Citation Context ...Axiom A9 (Nonatomicity). Every nonnull event can be partitioned into two nonnull events. Axiom A8” is stronger than Axiom A8 and is necessary to obtain a countably additive probability. Axiom A9 (see =-=Villegas, 1964-=-) is needed to obtain fineness and tightness of the qualitative probability. This leads to the following theorem: Axioms A1-A7, A8”, together with P2, P4, and A9 are necessary and sufficient for � to ... |

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Citation Context ...ater analytical tractability, multiplier, rather than constraint, preferences are used in the analysis of economic models (see, e.g., Woodford, 2006; Barillas et al., 2007; Karantounias et al., 2007; =-=Kleshchelski, 2007-=-). 10mula (7). Jacobson (1973), Whittle (1981), Skiadas (2003), and Maccheroni, Marinacci, and Rustichini (2006b) showed that in dynamic settings this link manifests itself as an observational equiva... |

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