Aspirational Preferences and Their Representation by Risk Measures

Brown, David B.; Giorgi, Enrico De; Sim, Melvyn

doi:10.1287/mnsc.1120.1537

Cited by 58 publications

(8 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By adopting the concept of satisficing measure (Brown et al 2012), we study two measures: 1) CVaR satisficing measure (CSM) which measures the highest confidence level η which guarantees CV aR η achieving the target; and 2) entropic satisficing measure (ESM) which measures the smallest risk tolerance level under which the certainty equivalent for an exponential utility function achieves the target.…”

Section: Discussionmentioning

confidence: 99%

The Impact of a Target on Newsvendor Decisions

Chen

Long

Perakis

2015

M&SOM

View full text Add to dashboard Cite

Goal achieving is a commonly observed phenomenon in practice, and it plays an important role in decision making. In this paper we investigate the impact of a target on newsvendor decisions. We take into account the risk and model the effect of a target by maximizing the satisficing measure of a newsvendor's profit with respect to that target. We study two satisficing measures: i) CVaR (Conditional Value at Risk) satisficing measure that evaluates the highest confidence level of CVaR achieving the target; and ii) entropic satisficing measure that assesses the smallest risk tolerance level under which the certainty equivalent for exponential utility function achieves the target. For both satisficing measures, we find that the optimal ordering quantity increases with the target level. We determine an optimal order quantity for a target based newsvendor and charactize its properties with respect to, for example, product's profit margin.

show abstract

Section: Discussionmentioning

confidence: 99%

The Impact of a Target on Newsvendor Decisions

Chen

Long

Perakis

2015

M&SOM

View full text Add to dashboard Cite

show abstract

“…Finally, it is natural to consider extending the analysis developed in this paper to more general measures that go beyond hypotheses 1-6 made in this paper. One such possibility is to consider aspiration measures introduced by Brown et al (2012) that are considerably more general than convex risk measures and are also well formalized. We note in the e-companion however that a direct application of the concept of a preference robust aspiration measure, i.e., evaluating a random payoff Z based on its worst-case aspiration level, does not lead to an insightful way of comparing random payoffs and identifying optimal risk mitigating strategies.…”

Section: Resultsmentioning

confidence: 99%

Minimizing Risk Exposure When the Choice of a Risk Measure Is Ambiguous

Delage

2018

Management Science

View full text Add to dashboard Cite

Abstract. Since the financial crisis of [2007][2008][2009], there has been a renewed interest in quantifying more appropriately the risks involved in financial positions. Popular risk measures such as variance and value-at-risk have been found inadequate because we now give more importance to properties such as monotonicity, convexity, translation invariance, positive homogeneity, and law invariance. Unfortunately, the challenge remains that it is unclear how to choose a risk measure that faithfully represents a decision maker's true risk attitude. In this work, we show that one can account precisely for (neither more nor less than) what we know of the risk preferences of an investor/policy maker when comparing and optimizing financial positions. We assume that the decision maker can commit to a subset of the above properties (the use of a law invariant convex risk measure for example) and that he can provide a series of assessments comparing pairs of potential risky payoffs. Given this information, we propose to seek financial positions that perform best with respect to the most pessimistic estimation of the level of risk potentially perceived by the decision maker. We present how this preference robust risk minimization problem can be solved numerically by formulating convex optimization problems of reasonable size. Numerical experiments on a portfolio selection problem, where the problem reduces to a linear program, will illustrate the advantages of accounting for the fact that the choice of a risk measure is ambiguous.

show abstract

“…Moreover, the optimal satisficing value is normalized in a bounded interval, usually [0, 1], which is natural and convenient to illustrate the ranking result. Finally, any satisficing measure can be reformulated mathematically as a dual problem of its corresponding risk measure, so that in Brown et al (2012), aspirational preference measure is developed as an expanded case for satisficing measure that can handle ambiguity without a given probability distribution; moreover, it possesses more general properties than satisficing measure. Computationally, these two risk metrics lead to the topics on solving risk constrained optimization problems, for example, CVaR constrained problem.…”

Section: Target-based Measurementioning

confidence: 99%

Data-driven satisficing measure and ranking

Huang

2019

Journal of the Operational Research Society

View full text Add to dashboard Cite

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations). Sandoy and Aven (2006) can solve problems generated by introducing or not introducing an underlying probability model. The pairwise comparison theory (also called Bradley-Terry-Luce (BTL) model) widely used in study the preference in decision making was introduced in Bradley and Terry (1952); Luce (2005). A Bayesian approximation method with BTL model in Weng and Lin (2011), is proposed for online ranking in team performance. However, these methodologies do not consider assessing the "risk" of the systems and have not provided a formal definition of risk that can be uniformly applied to wide range of systems. Bayesian approaches used inIn financial mathematics, "risk measure" is defined as a mapping function from a probability space to real number. Some fundamental research has been conducted motivating the definition of risk measure. In Ruszczynski and Shapiro (2006), the definitions and conditions for convex and coherent risk measures are developed, and conjugate duality reformulation of risk functions is proposed. Rockafellar and Uryasev (2000) give the detailed arguments on the most widely investigated coherent and law invariant risk measure-Conditional value-at-risk (CVaR) with corresponding reformulation and optimization problem illustration. CVaR is widely involved in optimization under uncertainty, and helps to improve the reliability of solutions against extremely high loss. Krokhmal et al. (2002) study the portfolio optimization problem with CVaR objective and constraints, and corresponding reformulation and discretization are demonstrated. In Dai et al. (2016), robust version CVaR is applied in portfolio selection problem, where sampled scenario returns are generated by a factor model with some asymmetric and uncertainty set. In Noyan and Rudolf (2013), multivariate CVaR constraint problem is studied based on polyhedral scalarization and second-order stochastic dominance, and a cut generation algorithm is proposed, where each cut is obtained by solving a mixed integer problem. Xu and Yu (2014) reformulate a stochastic nonlinear complementary problem with CVaR constraints, and propose a penalized smoothing sam...

show abstract

Aspirational Preferences and Their Representation by Risk Measures

Cited by 58 publications

References 50 publications

The Impact of a Target on Newsvendor Decisions

The Impact of a Target on Newsvendor Decisions

Minimizing Risk Exposure When the Choice of a Risk Measure Is Ambiguous

Data-driven satisficing measure and ranking

Contact Info

Product

Resources

About