scholarly journals A First-Price Sealed-Bid Asymmetric Auction When Two Bidders Have Respective CRRA and General Utility Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mingming Gong ◽  
Shulin Liu
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Existence And Uniqueness ◽  
Allocative Efficiency ◽  
Relative Risk Aversion ◽  
General Utility ◽  
Sealed Bid ◽  
Concave Utility Function ◽  
Asymmetric Auction ◽  
Price Auction

We study a first-price auction with two bidders where one bidder is characterized by a constant relative risk aversion utility function (i.e., a concave power function) while the other has a general concave utility function. We establish the existence and uniqueness of the optimal strategic markups and analyze the effects of one bidder’s risk aversion level on the optimal strategic markups of him and his opponent’s, the allocative efficiency of the auction, and the seller’s expected revenue, respectively.

Power Law with Exponential Cut‐off Utility

Metamorphosis ◽  
2014 ◽  
Vol 13 (1) ◽  
pp. 26-32
Author(s):  
Afreen Arif H. ◽  
T.P.M. Pakkala
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Power Law ◽  
Risk Preferences ◽  
Portfolio Allocation ◽  
Utility Functions ◽  
Relative Risk Aversion ◽  
Optimal Solutions ◽  
New Class ◽  
Exponential Power

Most of the utility functions studied earlier concentrated on properties of risk aversion. In this article, the authors have introduced a new class of utility function called the Power Law with Exponential Cut-off (PLEC) utility function, which exhibits all the absolute and relative risk aversion and risk loving preferences of individuals, under various conditions. It generalises and encompasses other systems of utility functions like that of exponential power. Certain properties of this utility function are discussed. Sensitivity analysis exhibits different portfolio allocations for various risk preferences. The analysis also shows that arbitrary risk preferences may lead to biased risk response estimates. Performance of PLEC utility function in portfolio allocation problem is demonstrated through numerical examples. This is evaluated through optimal solutions.

Inferring Risk Preferences Using Synthetic Win Bets in Horse Betting “Exotic” Markets

2013 ◽  
Vol 2 (1) ◽  
pp. 1-29
Author(s):  
Philip O'Connor
Keyword(s):  
Relative Risk ◽  
Standard Deviation ◽  
Risk Aversion ◽  
Financial Markets ◽  
Utility Function ◽  
Utility Theory ◽  
Risk Preferences ◽  
Higher Order ◽  
Relative Risk Aversion ◽  
Higher Order Moments

Exotic bets: exactas, trifectas and superfectas are complicated gambles that depend on the ordering of horse in a race that can be studied by converting them into “synthetic” or “virtual” win bets. Using two ways of constructing synthetic win bets, it is shown that the favorite-longshot bias is a poor description of the returns of the trifecta and superfecta synthetic win bet. Rather, consistent with financial markets, the standard deviation of the payout of the synthetic win bet better describes the different returns of synthetic win bets.It is found that the synthetic win market dislikes standard deviation and kurtosis (and other higher-order even moments) and likes skewness (and other higher order odd moments), implying participants conform to standard utility theory in their choice between win and synthetic win bets and are not risk-loving. A co-efficient of relative risk aversion of about 3 is estimated. Including higher-order moments strongly affects the magnitude of utility function estimates.

scholarly journals IDENTIFICATION AND ESTIMATION IN A THIRD-PRICE AUCTION MODEL

2019 ◽  
Vol 36 (3) ◽  
pp. 386-409
Author(s):  
Andreea Enache ◽  
Jean-Pierre Florens
Keyword(s):  
Risk Aversion ◽  
Surprising Result ◽  
The Third ◽  
Transaction Prices ◽  
Sealed Bid ◽  
Private Values ◽  
Price Auction ◽  
Global Identification ◽  
Auction Format ◽  
Auction Model

The first novelty of this paper is that we show global identification of the private values distribution in a sealed-bid third-price auction model using a fully nonparametric methodology. The second novelty of the paper comes from the study of the identification and estimation of the model using a quantile approach. We consider an i.i.d. private values environment with risk-averse bidders. In the first place, we consider the case where the risk-aversion parameter is known. We show that the speed of convergence in process of our nonparametric estimator produces at the root-n parametric rate, and we explain the intuition behind this apparently surprising result. Next, we consider that the risk-aversion parameter is unknown, and we locally identify it using exogenous variation in the number of participants. We extend our procedure to the case where we observe only the bids corresponding to the transaction prices, and we generalize the model so as to account for the presence of exogenous variables. The methodological toolbox used to analyse identification of the third-price auction model can be employed in the study of other games of incomplete information. Our results are interesting, also from a policy perspective, as some authors recommend the use of the third-price auction format for certain Internet auctions. Moreover, we contribute to the econometric literature on auctions using a quantile approach.

Relative Risk Aversion and Portfolio Choice

2005 ◽  
Author(s):  
Pablo Muñoz Ceballos ◽  
Esteban Flores Díaz
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Relative Risk Aversion

scholarly journals Relative risk aversion models: How plausible are their assumptions?

2021 ◽  
pp. 104346312199408
Author(s):  
Carlo Barone ◽  
Katherin Barg ◽  
Mathieu Ichou
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Loss Aversion ◽  
Educational Inequality ◽  
Risky Choice ◽  
Relative Risk Aversion ◽  
Downward Mobility ◽  
Educational Decisions ◽  
Empirically Supported ◽  
Occupational Risks

This work examines the validity of the two main assumptions of relative risk-aversion models of educational inequality. We compare the Breen-Goldthorpe (BG) and the Breen-Yaish (BY) models in terms of their assumptions about status maintenance motives and beliefs about the occupational risks associated with educational decisions. Concerning the first assumption, our contribution is threefold. First, we criticise the assumption of the BG model that families aim only at avoiding downward mobility and are insensitive to the prospects of upward mobility. We argue that the loss-aversion assumption proposed by BY is a more realistic formulation of status-maintenance motives. Second, we propose and implement a novel empirical approach to assess the validity of the loss-aversion assumption. Third, we present empirical results based on a sample of families of lower secondary school leavers indicating that families are sensitive to the prospects of both upward and downward mobility, and that the loss-aversion hypothesis of BY is empirically supported. As regards the risky choice assumption, we argue that families may not believe that more ambitious educational options entail occupational risks relative to less ambitious ones. We present empirical evidence indicating that, in France, the academic path is not perceived as a risky option. We conclude that, if the restrictive assumptions of the BG model are removed, relative-risk aversion needs not drive educational inequalities.

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