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. / Singapore-MIT Alliance (SMA)

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 98-104).

Activation of the immune system by e.g. bacteria induces the acute-phase-response and sickness behaviour. The latter encompasses among other things fever, lethargy, anorexia and hyperalgesia. An often used model to study sickness behaviour is the intravenous injection of the gram negative bacterial endotoxin lipopolysaccharide (LPS). LPS induces the production of inflammatory mediators, such as cytokines and prostaglandins, which in turn can interact with the central nervous system (CNS) to affect behaviour. The CNS also memorises substances that have made us sick in the past to avoid future harm, a phenomenon called conditioned taste aversion (CTA). An often used model to study CTA is the intraperitoneal injection of LiCl. The pontine parabrachial nucleus (PB) is an autonomic relay nucleus situated in the rostral brain stem that integrates afferent somatosensory and interoceptive information and forwards this information to the hypothalamus and limbic structures. PB is crucial for the acquisition of CTA and PB neurons are activated by many anorexigenic substances. Further, PB neurons express neuropeptides, among those calcitonin gene related peptide (CGRP) and enkephalin, both of which have been implicated in immune signalling, nociception, food intake, and aversion. By using a dual-labelling immunohistochemical/in situ hybridization technique we investigated if enkephalinergic neurons in PB are activated by systemic immune challenge. While there were many neurons in the external lateral parabrachial subnucleus (PBel) that expressed the immediate early gene fos after intravenous injection of LPS and while a large proportion of the PBel neurons expressed preproenkephalin, there were very few double-labelled cells. The fos-expressing cells were predominantly located to the outer part of the PBel (PBelo), whereas the preproenkephalin-expressing PBel neurons were located closest to the peduncle. Thus we conclude that although enkephalin has been implicated in autonomic and immune signalling, enkephalinergic neurons in PB do not seem to be activated by immune stimulation (paper I). To further characterise the PBelo neurons activated by immune challenge we investigated if these neurons expressed CGRP. Dual-labelling in situ hybridisation showed that PBelo neurons that expressed fos after intravenous injection of LPS to a large extent co-expressed CGRP mRNA, indicating that CGRP may be involved in the regulation of the sickness response in immune challenge (paper II). Using dual-labelling immunohistochemistry we examined if PBel neurons activated by an immune stimulus projected to the amygdala, a limbic structure implicated in the affective response to homeostatic challenge. Animals were injected with the retrograde tracer substance cholera toxin b (CTb) into the amygdala and subsequently subjected to immune challenge. We found that approximately a third of the neurons that expressed fos after the intravenous injection of LPS also were labelled with CTb. Thus PBel neurons activated by immune challenge project to the amygdala. The PBel-amygdala pathway has earlier been suggested to be important in nociceptive signalling. To investigate if amygdala-projecting PBel neurons are activated by nociceptive stimuli we again injected animals with CTb into the amygdala. After recovery the animals were injected with formalin into a hindpaw. Dual-labelling immunohistochemistry against fos and CTb showed that very few noxiously activated PB neurons projected to the amygdala. Thus, the PBel-amygdala projection seems to be important in immune challenge but not in nociceptive signalling (paper III). Many PBel neurons express fos after intraperitoneal injection of LiCl. Melanocortins are neuropeptides that recently have been implicated in metabolism, food intake and aversive mechanisms. The PB is known to express melanocortin receptor-4 (MC4-R) mRNA. Using dual-labelling in situ hybridization we investigated if PB neurons activated by intravenous injection of LPS or intraperitoneal injection of LiCl expressed MC4-R mRNA. We found that many PBelo neurons were activated by either LPS or LiCl and that a large proportion of such activated neurons expressed MC4-R mRNA. Further, using dual-labelling in situ hybridization against MC4-R mRNA and CGRP mRNA, we found that a large proportion of the CGRP positive PBelo neurons also expressed MC4-R mRNA. In summary, this thesis shows that CGRP-expressing neurons in the PBel are activated by peripheral immune challenge, that lipopolysaccharide-activated PBel neurons project to the amygdala, that the amygdala-projecting neurons in the PBel are CGRP-positive, and that PBel neurons activated by immune or aversive challenge express MC4-R. Taken together, these data suggest the presence of a melanocortin-regulated CGRP-positive pathway from the PBel to the amygdala that relays information of importance to certain aspects of sickness behaviour. / On the day of the defence date the title of article II was: Feeding-related immune responsive brain stem neurons: association with CGRP. Article II: Erratum for in Neuroreport 2001;12(16):inside back cover. Neuroreport 2001;12(13):inside back cover. Article III: Erratum in: J Comp Neurol. 2005; 483:489-90.

While the market for credit instruments grew continuously in the decade before 2008, its liquidity has dried up significantly in the current crisis, and investors have become aware of the possible consequences of being exposed to credit risk. In this thesis we address these issues by pricing credit instruments using utility indifference pricing, a method that takes into account the investor's personal risk aversion and which is not affected by the lack of liquidity. Through stochastic optimal control methods, we use indifference pricing with exponential utility to determine corporate bond prices and CDS spreads. In the first part we examine how these quantities are affected by risk aversion under different models of default. The emphasis lies on a hybrid model, in which a regime switch of the reference entity is triggered by a creditworthiness index correlated to its stock price. The second part generalizes this setup by introducing uncertainty in the model parameters. Robust optimal control has been used independently in the literature to address model uncertainty for portfolio selection problems. Here, we incorporate this approach with utility indifference and derive some analytical and numerical results on how model uncertainty affects credit spreads.

In previous research, aggregation of returns has been found as a way to counteract the risk averse behavior that is the result of investors' myopia. This paper expands the study of aggregation by analyzing its effect on forward looking probabilities. Namely, through the disaggregation of future information, subjects become myopic and trade with varying risk preferences. In an experimental market, subjects trading securities with disaggregated forward looking information are found to 'buy high and sell low', while subjects trading the same securities, but with aggregated information, trade with more consistent risk preferences.

While the market for credit instruments grew continuously in the decade before 2008, its liquidity has dried up significantly in the current crisis, and investors have become aware of the possible consequences of being exposed to credit risk. In this thesis we address these issues by pricing credit instruments using utility indifference pricing, a method that takes into account the investor's personal risk aversion and which is not affected by the lack of liquidity. Through stochastic optimal control methods, we use indifference pricing with exponential utility to determine corporate bond prices and CDS spreads. In the first part we examine how these quantities are affected by risk aversion under different models of default. The emphasis lies on a hybrid model, in which a regime switch of the reference entity is triggered by a creditworthiness index correlated to its stock price. The second part generalizes this setup by introducing uncertainty in the model parameters. Robust optimal control has been used independently in the literature to address model uncertainty for portfolio selection problems. Here, we incorporate this approach with utility indifference and derive some analytical and numerical results on how model uncertainty affects credit spreads.

The role of public transportation increases as travel demand increases due to the growth in population and economics. The importance of providing a balanced public transportation has increased. In Ontario, Canada, the provincial government investing more than $17B in transit projects by the year of 2020 [28]. Consequently, planners and engineers motivated to pay more attention to mode split (mode choice) models used to estimate transit ridership. In most existing mode choice models, the likelihood of a trip maker using a transit mode (e.g. transit) is based on the generalized cost (GC) of using transit mode relative to the generalized cost of all other available modes. In conventional generalized cost formulations, transit costs are considered deterministic. It is quite evident, however, that great variability exists in the reliability of transit service and, as a result, the actual costs experienced by users. Efforts are ongoing to incorporate the costs of reliability in mode choice models by extending formulations to include penalties for arriving prior to or later than a desired arrival time. Transit operators strive to provide reliable service to retain and attract more users. Unreliable service can adversely affect the user by arriving late or early at their destination, waiting longer at their boarding station, and spending more time than expected in the transit vehicle. Unreliable service will also increase the user's anxiety associated with the uncertainty and discomfort. All these factors should be considered explicitly within the generalized cost (GC) function in order to accurately capture the GC of transit service relative to other modes and to ensure that these factors are not incorporated within the mode specific constant. In this study, a GC model is developed that explicitly represents service reliability. Service reliability is represented in the model as penalties associated with passengers' late arrival, early arrival, departure time shifting, waiting time, and anxiety. Furthermore, a methodology of utilizing field data to capture service reliability is defined. A Monte-Carlo simulation framework has been developed using the proposed GC function to quantify the impact of transit reliability on transit user cost. The proposed framework was applied on the iXpress service in the Regional of Waterloo in Ontario, Canada, utilizing Automated Vehicle Location (AVL) system data from the Regional Municipality of Waterloo to estimate service reliability. All the coefficients included in the proposed GC are assumed based on the relative importance of each penalty to scheduled in vehicle time by considering different passenger classes. In this research, the transit passengers are assumed to belong to one of three passenger classes based on their risk tolerance. From the results, it was found that increasing reliability of arrivals at a station can decrease transit users generalized costs significantly. We further posit that including uncertainty in the calculation of generalized costs may provide better estimates for mode split in travel forecasting models.

The first chapter is based on a paper with Jin Li in fair division. It was recently discovered that on the domain of Leontief preferences, Hurwicz (1972)'s classic impossibility result does not hold; that is, one can find efficient, strategy-proof and individually rational rules to divide resources among agents. Here we consider the problem of dividing l divisible goods among n agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned. The second and third chapters are based on two working papers of mine in decision making under uncertainty. In the second chapter, I study the wealth effect under uncertainty --- how the wealth level impacts a decision maker's degree of uncertainty aversion. I axiomatize a class of preferences displaying decreasing absolute uncertainty aversion, which allows a decision maker to be more willing to take uncertainty-bearing behavior when he becomes wealthier. Three equivalent preference representations are obtained. The first is a variation on the constraint criterion of Hansen and Sargent (2001). The other two respectively generalize Gilboa and Schmeidler (1989)'s maxmin criterion and Maccheroni, Marinacci and Rustichini (2006)'s variational representation. This class, when restricted to preferences exhibiting constant absolute uncertainty aversion, is exactly Maccheroni, Marinacci and Rustichini (2006)'s ariational preferences. Thus, the results further enable us to establish relationships among the representations for several important classes within variational preferences. The three representations provide different decision rules to rationalize the same class of preferences. The three decision rules correspond to three ways which are proposed in the literature to identify a decision maker's perception about uncertainty and his attitude toward uncertainty. However, I give examples to show that these identifications conflict with each other. It means that there is much freedom in eliciting two unobservable and subjective factors, one's perception about and attitude toward uncertainty, from only his choice behavior. This exactly motivates the work in Chapter 3. In the third chapter, I introduce confidence orders in addition to preference orders. Axioms are imposed on both orders to reveal a decision maker's perception about uncertainty and to characterize the following decision rule. A decision maker evaluates an act based on his aspiration and his confidence in this aspiration. Each act corresponds to a trade-off line between the two criteria: The more he aspires, the less his confidence in achieving the aspiration level. The decision maker ranks an act by the optimal combination of aspiration and confidence on its trade-off line according to an aggregating preference of his over the two-criterion plane. The aggregating preference indicates his uncertainty attitude, while his perception about uncertainty is summarized by a generalized second-order belief over the prior space, and this belief is revealed by his confidence order.

The role of public transportation increases as travel demand increases due to the growth in population and economics. The importance of providing a balanced public transportation has increased. In Ontario, Canada, the provincial government investing more than $17B in transit projects by the year of 2020 [28]. Consequently, planners and engineers motivated to pay more attention to mode split (mode choice) models used to estimate transit ridership. In most existing mode choice models, the likelihood of a trip maker using a transit mode (e.g. transit) is based on the generalized cost (GC) of using transit mode relative to the generalized cost of all other available modes. In conventional generalized cost formulations, transit costs are considered deterministic. It is quite evident, however, that great variability exists in the reliability of transit service and, as a result, the actual costs experienced by users. Efforts are ongoing to incorporate the costs of reliability in mode choice models by extending formulations to include penalties for arriving prior to or later than a desired arrival time. Transit operators strive to provide reliable service to retain and attract more users. Unreliable service can adversely affect the user by arriving late or early at their destination, waiting longer at their boarding station, and spending more time than expected in the transit vehicle. Unreliable service will also increase the user's anxiety associated with the uncertainty and discomfort. All these factors should be considered explicitly within the generalized cost (GC) function in order to accurately capture the GC of transit service relative to other modes and to ensure that these factors are not incorporated within the mode specific constant. In this study, a GC model is developed that explicitly represents service reliability. Service reliability is represented in the model as penalties associated with passengers' late arrival, early arrival, departure time shifting, waiting time, and anxiety. Furthermore, a methodology of utilizing field data to capture service reliability is defined. A Monte-Carlo simulation framework has been developed using the proposed GC function to quantify the impact of transit reliability on transit user cost. The proposed framework was applied on the iXpress service in the Regional of Waterloo in Ontario, Canada, utilizing Automated Vehicle Location (AVL) system data from the Regional Municipality of Waterloo to estimate service reliability. All the coefficients included in the proposed GC are assumed based on the relative importance of each penalty to scheduled in vehicle time by considering different passenger classes. In this research, the transit passengers are assumed to belong to one of three passenger classes based on their risk tolerance. From the results, it was found that increasing reliability of arrivals at a station can decrease transit users generalized costs significantly. We further posit that including uncertainty in the calculation of generalized costs may provide better estimates for mode split in travel forecasting models.

Studies in newsvendor decision-making have shown that human decisions systematically deviate from analytical solutions found in many utility models of the single period problem (SPP). Yet for the most part the impacts of this human decision bias in systems of newsvendor type products have not been investigated. We study bias in human decision-making to determine how different factors affect the performance of systems of newsvendor type products. We extended the state of the arts utility models of SPP to analyze the effects of individuals wealth on individual decision-making. Our theoretical and empirical results proved that individuals wealth significantly affected individual decision-making. Specifically, our analysis concluded that wealthier individual ordered more than poorer individual did when presented with the same investment opportunity. We created a human decision bias (HDB) model to include different newsvendor ordering policies that individuals could use to determine their order quantities. This model is set up to investigate individuals reliance on different ordering policies under different experimental conditions. We designed multi period newsvendor experiments to study effects of factors such as item profit margin, wealth, value of learning, and salvage value on decision-maker's order quantity. We found that wealth and profit margin factors significantly affected individual newsvendor decision-making. Learning, gender, and salvage value factor did not exhibit significant effects in our empirical studies. We designed multi period multi echelon newsvendor experiments to study effects of factors such as the relationship between newsvendors, item profit margin, and newsvendors' wealth on the performance of two-echelon newsvendors system. We found item profit margin, wealth, and relationship between supplier and retailer to significantly affect newsvendor decision-making. Finally, we present a case study of US fresh produce industry to illustrate the impacts of human decision bias on the performance of a supply chain system.