The Comparative Statics of Deductible Insurance in Expected- and Non-Expected-Utility Theories

1995 ◽  
Vol 20 (1) ◽  
pp. 57-72 ◽  
Author(s):  
Edward E. Schlee
Keyword(s):  
Expected Utility ◽  
Comparative Statics ◽  
Deductible Insurance

A Non‐Bayesian Theory of State‐Dependent Utility

Econometrica ◽  
2019 ◽  
Vol 87 (4) ◽  
pp. 1341-1366 ◽  
Author(s):  
Brian Hill
Keyword(s):  
Expected Utility ◽  
State Dependence ◽  
Comparative Statics ◽  
Bayesian Theory ◽  
Subjective Expected Utility ◽  
State Dependent ◽  
Special Cases

Many decision situations involve two or more of the following divergences from subjective expected utility: imprecision of beliefs (or ambiguity), imprecision of tastes (or multi‐utility), and state dependence of utility. This paper proposes and characterizes a model of uncertainty averse preferences that can simultaneously incorporate all three phenomena. The representation supports a principled separation of (imprecise) beliefs and (potentially state‐dependent, imprecise) tastes. Moreover, the representation permits comparative statics separating the roles of beliefs and tastes, and is modular: it easily delivers special cases involving various combinations of the phenomena, as well as state‐dependent multi‐utility generalizations covering popular ambiguity models.

scholarly journals Pessimistic Portfolio Choice with One Safe and One Risky Asset and Right Monotone Probability Difference Order

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jiangfeng Li ◽  
Qiong Wu ◽  
Zhiqiang Ye ◽  
Shunming Zhang
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Comparative Statics ◽  
Risky Asset ◽  
Stochastic Orders ◽  
Monotone Likelihood Ratio ◽  
Changes In Risk ◽  
The Right ◽  
Monotone Probability ◽  
The Relationship

As is well known, a first-order dominant deterioration in risk does not necessarily cause a risk-averse investor to reduce his holdings of that deteriorated asset under the expected utility framework, even in the simplest portfolio setting with one safe asset and one risky asset. The purpose of this paper is to derive conditions on shifts in the distribution of the risky asset under which the counterintuitive conclusion above can be overthrown under the rank-dependent expected utility framework, a more general and prominent alternative of the expected utility. Two new criterions of changes in risk, named the monotone probability difference (MPD) and the right monotone probability difference (RMPD) order, are proposed, which is a particular case of the first stochastic dominance. The relationship among MPD, RMPD, and the other two important stochastic orders, monotone likelihood ratio (MLR) and monotone probability ratio (MPR), is examined. A desired comparative statics result is obtained when a shift in the distribution of the risky asset satisfies the RMPD criterion.

Alternative Approaches to Comparative nth-Degree Risk Aversion

2019 ◽  
Vol 65 (8) ◽  
pp. 3824-3834 ◽  
Author(s):  
Liqun Liu ◽  
William S. Neilson
Keyword(s):  
Risk Aversion ◽  
Decision Analysis ◽  
Expected Utility ◽  
Risk Premium ◽  
Higher Order ◽  
Comparative Statics ◽  
Risk Increase ◽  
Comparative Risk ◽  
Alternative Approaches ◽  
Comparative Risk Aversion

This paper extends the three main approaches to comparative risk aversion—the risk premium approach and the probability premium approach of Pratt (1964) [Risk aversion in the small and in the large. Econometrica 32(1-2):122–136] and the comparative statics approach of Jindapon and Neilson (2007) [Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach. J. Econom. Theory 136(1):719–728]—to study comparative nth-degree risk aversion. These extensions can accommodate trading off an nth-degree risk increase and an mth-degree risk increase for any m, such that [Formula: see text]. It goes on to show that, in the expected utility framework, all of these general notions of comparative nth-degree risk aversion are equivalent and can be characterized by the concept of (n/m)th-degree Ross more risk aversion of Liu and Meyer (2013) [Substituting one risk increase for another: A method for measuring risk aversion. J. Econom. Theory 148(6):2706–2718]. This paper was accepted by Han Bleichrodt, decision analysis.

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