scholarly journals An Optimal Decision Rule for a Multiple Selling Problem with a Variable Rate of Offers

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 690 ◽  
Author(s):  
Georgy Sofronov
Keyword(s):  
Variable Number ◽  
Optimal Decision ◽  
Backward Induction ◽  
Variable Rate ◽  
Time Period ◽  
Optimal Decision Rule ◽  
Optimal Stopping Theory ◽  
Independent Observations ◽  
Expected Revenue ◽  
Finite Time Horizon

An asset selling problem is one of well-known problems in the decision making literature. The problem assumes a stream of bidders who would like to buy one or several identical objects (assets). Offers placed by the bidders once rejected cannot be recalled. The seller is interested in an optimal selling strategy that maximizes the total expected revenue. In this paper, we consider a multi-asset selling problem when the seller wants to sell several identical assets over a finite time horizon with a variable number of offers per time period and no recall of past offers. We consider the problem within the framework of the optimal stopping theory. Using the method of backward induction, we find an optimal sequential procedure which maximizes the total expected revenue in the selling problem with independent observations.

scholarly journals Optimal control of queueing networks: an approach via fluid models

2002 ◽  
Vol 34 (02) ◽  
pp. 313-328
Author(s):  
Nicole Bäuerle
Keyword(s):  
Optimal Control ◽  
Decision Rule ◽  
Average Cost ◽  
Queueing Networks ◽  
Optimal Decision ◽  
Stochastic Network ◽  
Asymptotically Optimal ◽  
Multiclass Queueing Networks ◽  
Optimal Decision Rule ◽  
Multiclass Queueing

We consider a general control problem for networks with linear dynamics which includes the special cases of scheduling in multiclass queueing networks and routeing problems. The fluid approximation of the network is used to derive new results about the optimal control for the stochastic network. The main emphasis lies on the average-cost criterion; however, the β-discounted as well as the finite-cost problems are also investigated. One of our main results states that the fluid problem provides a lower bound to the stochastic network problem. For scheduling problems in multiclass queueing networks we show the existence of an average-cost optimal decision rule, if the usual traffic conditions are satisfied. Moreover, we give under the same conditions a simple stabilizing scheduling policy. Another important issue that we address is the construction of simple asymptotically optimal decision rules. Asymptotic optimality is here seen with respect to fluid scaling. We show that every minimizer of the optimality equation is asymptotically optimal and, what is more important for practical purposes, we outline a general way to identify fluid optimal feedback rules as asymptotically optimal. Last, but not least, for routeing problems an asymptotically optimal decision rule is given explicitly, namely a so-called least-loaded-routeing rule.

The optimal decision rule in the Kiefer-Weiss problem for a Brownian motion

2013 ◽  
Vol 68 (2) ◽  
pp. 389-391
Author(s):  
Mikhail V Zhitlukhin ◽  
Alexey A Muravlev ◽  
Albert N Shiryaev
Keyword(s):  
Brownian Motion ◽  
Decision Rule ◽  
Optimal Decision ◽  
Optimal Decision Rule

scholarly journals Long-term evolution and seasonal modulation of methanol above Jungfraujoch (46.5° N, 8.0° E): optimisation of the retrieval strategy, comparison with model simulations and independent observations

2014 ◽  
Vol 7 (5) ◽  
pp. 4659-4692 ◽  
Author(s):  
W. Bader ◽  
T. Stavrakou ◽  
J.-F. Muller ◽  
S. Reimann ◽  
C. D. Boone ◽  
...  
Keyword(s):  
Peak Amplitude ◽  
Systematic Bias ◽  
Retrieval Strategy ◽  
Model Simulations ◽  
Term Evolution ◽  
Time Period ◽  
Independent Observations ◽  
June July

Abstract. Methanol (CH3OH) is the second most abundant organic compound in the Earth's atmosphere after methane. In this work, we present the first long-term time series of methanol total, lower tropospheric and upper tropospheric-lower stratospheric partial columns derived from the analysis of high resolution Fourier transform infrared solar spectra recorded at the Jungfraujoch station (46.5° N, 3580 m a.s.l.). The retrieval of methanol is very challenging due to strong absorptions of ozone in the region of the selected υ8 band of CH3OH. Two wide spectral intervals have been defined and adjusted in order to maximize the information content. Methanol does not exhibit a significant trend over the 1995–2012 time period, but a strong seasonal modulation characterized by maximum values and variability in June–July, minimum columns in winter and a peak-to-peak amplitude of 130%. In situ measurements performed at the Jungfraujoch and ACE-FTS occultations give similar results for the methanol seasonal variation. The total and lower tropospheric columns are also compared with IMAGESv2 model simulations. There is no systematic bias between the observations and IMAGESv2 but the model underestimates the peak-to-peak amplitude of the seasonal modulations.

scholarly journals Cognitive Imprecision and Small-Stakes Risk Aversion

2020 ◽  
Author(s):  
Mel Win Khaw ◽  
Ziang Li ◽  
Michael Woodford
Keyword(s):  
Risk Aversion ◽  
Mental Representation ◽  
Numerical Cognition ◽  
Quantitative Model ◽  
Perceptual Bias ◽  
Optimal Decision ◽  
Model Risk ◽  
Perceptual Judgments ◽  
Optimal Decision Rule ◽  
Expected Utility Maximization

Abstract Observed choices between risky lotteries are difficult to reconcile with expected utility maximization, both because subjects appear to be too risk averse with regard to small gambles for this to be explained by diminishing marginal utility of wealth, as stressed by Rabin (2000), and because subjects’ responses involve a random element. We propose a unified explanation for both anomalies, similar to the explanation given for related phenomena in the case of perceptual judgments: they result from judgments based on imprecise (and noisy) mental representations of the decision situation. In this model, risk aversion results from a sort of perceptual bias—but one that represents an optimal decision rule, given the limitations of the mental representation of the situation. We propose a quantitative model of the noisy mental representation of simple lotteries, based on other evidence regarding numerical cognition, and test its ability to explain the choice frequencies that we observe in a laboratory experiment.

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