Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.

A risk-averse optimization model for trading wind energy in a market environment under uncertainty

In this paper, a stochastic programming approach is proposed for trading wind energy in a market environment under uncertainty. Uncertainty in the energy market prices is the main cause of high volatility of profits achieved by power producers. The volatile and intermittent nature of wind energy represents another source of uncertainty. Hence, each uncertain parameter is modeled by scenarios, where each scenario represents a plausible realization of the uncertain parameters with an associated occurrence probability. Also, an appropriate risk measurement is considered. The proposed approach is applied on a realistic case study, based on a wind farm in Portugal. Finally, conclusions are duly drawn. (C) 2011 Elsevier Ltd. All rights reserved.

Avoiding the dark side of positive online consumer reviews: enhancing reviews' usefulness for high risk-averse travelers

The influence of positive online consumer reviews on a traveler's decision making remains unclear. To better understand the perceived usefulness of online reviews, this study conducts two experiments using positive and negative online consumer reviews. Study results suggest that high risk-averse travelers find negative online reviews more useful than positive reviews. For positive online reviews, high-risk averse travelers feel expert reviewers' postings, travel product pictures, and well-known brand names enhance usefulness of the positive online reviews. These findings offer interesting implications for both marketing theory and practice.

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Price stabilization and the risk-averse firm

An analytically simple and tractable approach to firm-level welfare analysis of complete and partial mean-preserving price stabilization for producers with general risk-averse preferences facing a stochastic technology is developed. Necessary and sufficient conditions for price stabilization to be welfare enhancing are derived under different assumptions of the producer's preferences and the producer's technology. Existing stabilization results for the risk-averse firm are shown to be corollaries of these more general results.

Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints

In this work we extend to the multistage case two recent risk averse measures for two-stage stochastic programs based on first- and second-order stochastic dominance constraints induced by mixed-integer linear recourse. Additionally, we consider Time Stochastic Dominance (TSD) along a given horizon. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by those risk measures, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-artMIP solver is also reported.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution.

Risk management for mathematical optimization under uncertainty

We present a general multistage stochastic mixed 0-1 problem where the uncertainty appears everywhere in the objective function, constraints matrix and right-hand-side. The uncertainty is represented by a scenario tree that can be a symmetric or a nonsymmetric one. The stochastic model is converted in a mixed 0-1 Deterministic Equivalent Model in compact representation. Due to the difficulty of the problem, the solution offered by the stochastic model has been traditionally obtained by optimizing the objective function expected value (i.e., mean) over the scenarios, usually, along a time horizon. This approach (so named risk neutral) has the inconvenience of providing a solution that ignores the variance of the objective value of the scenarios and, so, the occurrence of scenarios with an objective value below the expected one. Alternatively, we present several approaches for risk averse management, namely, a scenario immunization strategy, the optimization of the well known Value-at-Risk (VaR) and several variants of the Conditional Value-at-Risk strategies, the optimization of the expected mean minus the weighted probability of having a "bad" scenario to occur for the given solution provided by the model, the optimization of the objective function expected value subject to stochastic dominance constraints (SDC) for a set of profiles given by the pairs of threshold objective values and either bounds on the probability of not reaching the thresholds or the expected shortfall over them, and the optimization of a mixture of the VaR and SDC strategies.

Within-subject intra- and inter-method consistency of two experimental risk attitude elicitation methods

We compare the consistency of choices in two methods to used elicit risk preferences on an aggregate as well as on an individual level. We asked subjects to choose twice from a list of nine decision between two lotteries, as introduced by Holt and Laury (2002, 2005) alternating with nine decisions using the budget approach introduced by Andreoni and Harbaugh (2009). We find that while on an aggregate(subject pool) level the results are (roughly) consistent, on an individual(within-subject) level,behavior is far from consistent. Within each method as well as across methods we observe low correlations. This again questions the reliability of experimental risk elicitation measures and the ability to use results from such methods to control for the risk aversion of subjects when explaining e�ects in other experimental games.

Cortisol shifts financial risk preferences

Risk taking is central to human activity. Consequently, it lies at the focal point of behavioral sciences such as neuroscience, economics, and finance. Many influential models from these sciences assume that financial risk preferences form a stable trait. Is this assumption justified and, if not, what causes the appetite for risk to fluctuate? We have previously found that traders experience a sustained increase in the stress hormone cortisol when the amount of uncertainty, in the form of market volatility, increases. Here we ask whether these elevated cortisol levels shift risk preferences. Using a double-blind, placebo-controlled, cross-over protocol we raised cortisol levels in volunteers over eight days to the same extent previously observed in traders. We then tested for the utility and probability weighting functions underlying their risk taking, and found that participants became more risk averse. We also observed that the weighting of probabilities became more distorted among men relative to women. These results suggest that risk preferences are highly dynamic. Specifically, the stress response calibrates risk taking to our circumstances, reducing it in times of prolonged uncertainty, such as a financial crisis. Physiology-induced shifts in risk preferences may thus be an under-appreciated cause of market instability.

An evaluation of the effectiveness of Value-at-Risk (VaR) models for Australian banks under Basel III

This study compares Value-at-Risk (VaR) measures for Australian banks over a period that includes the Global Financial Crisis (GFC) to determine whether the methodology and parameter selection are important for capital adequacy holdings that will ultimately support a bank in a crisis period. VaR methodology promoted under Basel II was largely criticised during the GFC for its failure to capture downside risk. However, results from this study indicate that 1-year parametric and historical models produce better measures of VaR than models with longer time frames. VaR estimates produced using Monte Carlo simulations show a high percentage of violations but with lower average magnitude of a violation when they occur. VaR estimates produced by the ARMA GARCH model also show a relatively high percentage of violations, however, the average magnitude of a violation is quite low. Our findings support the design of the revised Basel II VaR methodology which has also been adopted under Basel III.

Critical risk factors affecting the implementation of PPP waste-to-energy projects in China

Since 2003, Mainland China has been promoting the public–private partnership (PPP) procurement model in the waste-to-energy incineration sector to reduce the waste burying rate and improve environmental quality. Five critical risk factors (CRFs) that affect the construction and operation of waste-to-energy incineration projects have been identified from real-life risk events of 14 PPP waste-to-energy incineration plants through content analysis. These risk factors are insufficient waste supply, disposal of non-licensed waste, environmental risk, payment risk, and lack of supporting infrastructure. A recently completed PPP waste-to-energy incineration plant, the Shanghai Tianma project, was investigated to learn from the effective management of CRFs. First-hand data about the Shanghai Tianma project was collected, with a focus on project negotiation and concession agreement. Lessons learned about risk management were acquired. This paper presents a detailed study of the contractual structure, risk sharing scheme, risk response measures to CRFs, and project transfer of a PPP project. The study results will provide governments with management implications to prepare equitable concession agreements and benefit private investors by effectively mitigating and managing risks in future PPP waste-to-energy incineration projects.

Flood risk management: What are the main drivers of prevention?

4 p.

Essays in revealed preference theory and behavioral economics

Time, risk, and attention are all integral to economic decision making. The aim of this work is to understand those key components of decision making using a variety of approaches: providing axiomatic characterizations to investigate time discounting, generating measures of visual attention to infer consumers' intentions, and examining data from unique field settings.

Chapter 2, co-authored with Federico Echenique and Kota Saito, presents the first revealed-preference characterizations of exponentially-discounted utility model and its generalizations. My characterizations provide non-parametric revealed-preference tests. I apply the tests to data from a recent experiment, and find that the axiomatization delivers new insights on a dataset that had been analyzed by traditional parametric methods.

Chapter 3, co-authored with Min Jeong Kang and Colin Camerer, investigates whether "pre-choice" measures of visual attention improve in prediction of consumers' purchase intentions. We measure participants' visual attention using eyetracking or mousetracking while they make hypothetical as well as real purchase decisions. I find that different patterns of visual attention are associated with hypothetical and real decisions. I then demonstrate that including information on visual attention improves prediction of purchase decisions when attention is measured with mousetracking.

Chapter 4 investigates individuals' attitudes towards risk in a high-stakes environment using data from a TV game show, Jeopardy!. I first quantify players' subjective beliefs about answering questions correctly. Using those beliefs in estimation, I find that the representative player is risk averse. I then find that trailing players tend to wager more than "folk" strategies that are known among the community of contestants and fans, and this tendency is related to their confidence. I also find gender differences: male players take more risk than female players, and even more so when they are competing against two other male players.

Chapter 5, co-authored with Colin Camerer, investigates the dynamics of the favorite-longshot bias (FLB) using data on horse race betting from an online exchange that allows bettors to trade "in-play." I find that probabilistic forecasts implied by market prices before start of the races are well-calibrated, but the degree of FLB increases significantly as the events approach toward the end.