Technical Note—Time Inconsistency of Optimal Policies of Distributionally Robust Inventory Models

2020 ◽  
Vol 68 (5) ◽  
pp. 1576-1584 ◽  
Author(s):  
Alexander Shapiro ◽  
Linwei Xin

The authors extend previous studies of time inconsistency to risk averse (distributionally robust) inventory models and show that time inconsistency is not unique to robust multistage decision making, but may happen for a large class of risk averse/distributionally robust settings. In particular, they demonstrate that if the respective risk measures are not strictly monotone, then there may exist infinitely many optimal policies which are not base-stock and not time consistent. This is in a sharp contrast with the risk neutral formulation of the inventory model where all optimal policies are base-stock and time consistent.

2021 ◽  
Author(s):  
Alois Pichler ◽  
Rui Peng Liu ◽  
Alexander Shapiro

This paper addresses time consistency of risk-averse optimal stopping in stochastic optimization. It is demonstrated that time-consistent optimal stopping entails a specific structure of the functionals describing the transition between consecutive stages. The stopping risk measures capture this structural behavior and allow natural dynamic equations for risk-averse decision making over time. Consequently, associated optimal policies satisfy Bellman’s principle of optimality, which characterizes optimal policies for optimization by stating that a decision maker should not reconsider previous decisions retrospectively. We also discuss numerical approaches to solving such problems.


2014 ◽  
Vol 44 (2) ◽  
pp. 277-302 ◽  
Author(s):  
Christian Y. Robert ◽  
Pierre-E. Therond

AbstractWe consider the class of concave distortion risk measures to study how choice is influenced by the decision-maker's attitude to risk and provide comparative statics results. We also assume ambiguity about the probability distribution of the risk and consider a framework à la Klibanoff, Marinacci and Mukerji (2005; A smooth model of decision making under ambiguity.Econometrica,73, 1849–1892) to study the value of information that resolves ambiguity. We show that this value increases with greater ambiguity, with greater ambiguity aversion, and in some cases with greater risk aversion. Finally, we examine whether a more risk-averse and a more ambiguity-averse individual will invest in more effort to shift his initial risk distribution to a better target distribution.


Author(s):  
Nilay Noyan ◽  
Gábor Rudolf ◽  
Miguel Lejeune

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.


Risks ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 115
Author(s):  
Despoina Makariou ◽  
Pauline Barrieu ◽  
George Tzougas

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.


Author(s):  
Ming-Sheng Ying ◽  
Yuan Feng ◽  
Sheng-Gang Ying

AbstractMarkov decision process (MDP) offers a general framework for modelling sequential decision making where outcomes are random. In particular, it serves as a mathematical framework for reinforcement learning. This paper introduces an extension of MDP, namely quantum MDP (qMDP), that can serve as a mathematical model of decision making about quantum systems. We develop dynamic programming algorithms for policy evaluation and finding optimal policies for qMDPs in the case of finite-horizon. The results obtained in this paper provide some useful mathematical tools for reinforcement learning techniques applied to the quantum world.


2009 ◽  
Vol 104 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Wen-Bin Chiou ◽  
Ming-Hsu Chang ◽  
Chien-Lung Chen

Raghunathan and Pham conducted a pioneer study in 1999 on the motivational influences of anxiety and sadness on decision making and indicated that anxiety would motivate individuals to be risk averse, whereas sadness would motivate individuals to be risk taking. A replication study was employed in the domain of perceived travel risk. Compared to participants in a neutral mood, anxious participants showed higher perceived travel risk than sad participants. Moreover, the differential effect of anxiety and sadness on perceived travel risk was only pronounced under the high personal relevance condition, in which participants made personal decisions and expected that they would be affected by the outcomes. In general, the results extend the notion proposed by Raghunathan and Pham suggesting that travelers' implicit goals primed by anxiety or sadness used for mood-repair purposes appear to be moderated by personal relevance.


Criminology ◽  
2021 ◽  
Author(s):  
James C. Oleson

The evidence-based practice (EBP) movement can be traced to a 1992 article in the Journal of the American Medical Association, although decision-making with empirical evidence (rather than tradition, anecdote, or intuition) is obviously much older. Neverthless, for the last twenty-five years, EBP has played a pivotal role in criminal justice, particularly within community corrections. While the prediction of recidivism in parole or probation decisions has attracted relatively little attention, the use of risk measures by sentencing judges is controversial. This might be because sentencing typically involves both backward-looking decisions, related to the blameworthiness of the crime, as well as forward-looking decisions, about the offender’s prospective risk of recidivism. Evidence-based sentencing quantifies the predictive aspects of decision-making by incorporating an assessment of risk factors (which increase recidivism risk), protective factors (which reduce recidivism risk), criminogenic needs (impairments that, if addressed, will reduce recidivism risk), the measurement of recidivism risk, and the identification of optimal recidivism-reducing sentencing interventions. Proponents for evidence-based sentencing claim that it can allow judges to “sentence smarter” by using data to distinguish high-risk offenders (who might be imprisoned to mitigate their recidivism risk) from low-risk offenders (who might be released into the community with relatively little danger). This, proponents suggest, can reduce unnecessary incarceration, decrease costs, and enhance community safety. Critics, however, note that risk assessment typically looks beyond criminal conduct, incorporating demographic and socioeconomic variables. Even if a risk factor is facially neutral (e.g., criminal history), it might operate as a proxy for a constitutionally protected category (e.g., race). The same objectionable variables are used widely in presentence reports, but their incorporation into an actuarial risk score has greater potential to obfuscate facts and reify underlying disparities. The evidence-based sentencing literature is dynamic and rapidly evolving, but this bibliography identifies sources that might prove useful. It first outlines the theoretical foundations of traditional (non-evidence-based) sentencing, identifying resources and overviews. It then identifies sources related to decision-making and prediction, risk assessment logic, criminogenic needs, and responsivity. The bibliography then describes and defends evidence-based sentencing, and identifies works on sentencing variables and risk assessment instruments. It then relates evidence-based sentencing to big data and identifies data issues. Several works on constitutional problems are listed, the proxies problem is described, and sources on philosophical issues are described. The bibliography concludes with a description of validation research, the politics of evidence-based sentencing, and the identification of several current initiatives.


2013 ◽  
Vol 50 (02) ◽  
pp. 533-541 ◽  
Author(s):  
Alexander Shapiro

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.


Sign in / Sign up

Export Citation Format

Share Document