Weighted Almost Stochastic Dominance: Revealing the Preferences of Most Decision Makers in the St. Petersburg Paradox

2015 ◽  
Vol 12 (2) ◽  
pp. 74-80 ◽  
Author(s):  
Chin Hon Tan
Keyword(s):  
Stochastic Dominance ◽  
Decision Makers ◽  
Almost Stochastic Dominance ◽  
Petersburg Paradox

Estimating the Critical Parameter in Almost Stochastic Dominance from Insurance Deductibles

2020 ◽  
Author(s):  
Yi-Chieh Huang ◽  
Kamhon Kan ◽  
Larry Y. Tzeng ◽  
Kili C. Wang
Keyword(s):  
Real World ◽  
Upper Bound ◽  
Stochastic Dominance ◽  
Critical Parameter ◽  
Experimental Studies ◽  
Decision Makers ◽  
The Other ◽  
Real World Data ◽  
Upper Bound Estimate ◽  
Almost Stochastic Dominance

Knowing how small a violation of stochastic dominance rules would be accepted by most individuals is a prerequisite to applying almost stochastic dominance criteria. Unlike previous laboratory-experimental studies, this paper estimates an acceptable violation of stochastic dominance rules with 939,690 real world data observations on a choice of deductibles in automobile theft insurance. We find that, for all policyholders in the sample who optimally chose a low deductible, the upper bound estimate of the acceptable violation ratio is 0.0014, which is close to zero. On the other hand, considering that most decision makers, such as 99% (95%) of the policyholders in the sample, optimally chose the low deductible, the upper bound estimate of the acceptable violation ratio is 0.0405 (0.0732). Our results provide reference values for the acceptable violation ratio for applying almost stochastic dominance rules. This paper was accepted by Manel Baucells, decision analysis.

Almost Stochastic Dominance for Most Risk-Averse Decision Makers

2020 ◽  
Vol 17 (2) ◽  
pp. 169-184
Author(s):  
Chunling Luo ◽  
Chin Hon Tan
Keyword(s):  
Closed Form ◽  
Stochastic Dominance ◽  
Decision Makers ◽  
Risk Averse ◽  
Clear Insight ◽  
Mean And Variance ◽  
Expected Values ◽  
The Difference ◽  
Almost Stochastic Dominance ◽  
Insight Into

In this paper, we propose a new concept of almost second-degree stochastic dominance (ASSD), which we term almost risk-averse stochastic dominance (ARSD). Compared with existing ASSD conditions, ARSD can exclude extremely risk-averse utility functions. Hence, ARSD is able to reveal clear preferences of most risk-averse decision makers in practice, which are otherwise unable to be revealed. The simple closed-form of ARSD not only makes it easy to use in practice but also provides a clear insight into the preferences of decision makers and the difference in expected values and stochastic dominance violations. Moreover, we show that ARSD can be inferred based on mean and variance alone, and thus it is applicable even when distribution information is incomplete.

scholarly journals The concept of stochastic dominance in ranking investment alternatives

2005 ◽  
Vol 50 (164) ◽  
pp. 135-149
Author(s):  
Dejan Trifunovic
Keyword(s):  
Stochastic Dominance ◽  
Distribution Functions ◽  
Third Order ◽  
Ranking Problem ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Arbitrage Opportunities ◽  
Second Order Stochastic Dominance ◽  
Mean Variance ◽  
Almost Stochastic Dominance

In order to rank investments under uncertainty, the most widely used method is mean variance analysis. Stochastic dominance is an alternative concept which ranks investments by using the whole distribution function. There exist three models: first-order stochastic dominance is used when the distribution functions do not intersect, second-order stochastic dominance is applied to situations where the distribution functions intersect only once, while third-order stochastic dominance solves the ranking problem in the case of double intersection. Almost stochastic dominance is a special model. Finally we show that the existence of arbitrage opportunities implies the existence of stochastic dominance, while the reverse does not hold.

Bounded, Sigmoid Utility for Insurance Applications

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Siwei Gao ◽  
Michael R. Powers
Keyword(s):  
Decision Maker ◽  
Utility Functions ◽  
Decision Makers ◽  
Logical Necessity ◽  
Empirical Observation ◽  
Von Neumann ◽  
Bid Price ◽  
Bounded Below ◽  
Petersburg Paradox ◽  
Actual Decision

AbstractApplying a well-known argument of Karl Menger to an insurance version of the St. Petersburg Paradox (in which the decision maker is confronted with losses, rather than gains), one can assert that von Neumann-Morgenstern utility functions are necessarily concave upward and bounded below as decision-maker wealth tends to negative infinity. However, this argument is subject to two potential criticisms: (1) infinite-mean losses do not exist in the real world; and (2) the St. Petersburg Paradox derives its force from empirical observation (i. e., that actual decision makers would not agree to an arbitrarily large insurance bid price to transfer an infinite-mean loss), and thus does not impart logical necessity. In the present article, these two criticisms are addressed in turn. We first show that, although infinite-mean insurance losses technically do not exist, they do provide a reasonable model for certain large (i. e., excess and reinsurance) property-liability indemnities. We then employ the Two-Envelope Paradox to demonstrate the logical necessity of concave-upward, lower-bounded utility for arbitrarily small (i. e., negative) values of wealth. Finally, we note that recognizing the bounded, sigmoid nature of utility functions challenges certain fundamental understandings in the economics of insurance demand, and can lead to vastly different conclusions regarding the bid price for insurance.

scholarly journals Bivariate almost stochastic dominance

2014 ◽  
Vol 57 (2) ◽  
pp. 377-405 ◽  
Author(s):  
Michel M. Denuit ◽  
Rachel J. Huang ◽  
Larry Y. Tzeng
Keyword(s):  
Stochastic Dominance ◽  
Almost Stochastic Dominance
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