optimal dynamic pricing for perishable assets with nonhomogeneous demand we consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon customers whose reservation price distribution changes over time arrive according to a nonhomogeneous poisson process we show that at any given time the optimal price decreases with inventory we also identify a sufficient condition under which the optimal price decreases over time for a given inventory level this sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time in addition to shedding managerial insight these structural properties enable efficient computation of the optimal policy numerical studies are conducted to show the revenue impact of dynamic price policies price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price for the former our examples show that using optimal dynamic optimal policies achieves 2 4 7 3 revenue improvement over the optimal single price policy for the latter the revenue increase can be as high as 100 these results explain why yield management has become so essential to fashion retailing and travel service industries

explaining fashion cycles imitators chasing innovators in product space abstract this paper considers the problem of a fashion trend setter confronting an imitator who can produce the same product at lower cost a one dimensional product space is considered which is an abstraction of the key attribute of some consumer good three broad strategies can be optimal for the fashion leader 1 never innovate which milk profits from the initially advantageous position but ultimately concede the market without a fight 2 innovate once but only once which just temporarily defers conceding the market 3 cycle infinitely around product space never letting the imitator catch up and capture the market sometimes the cycles start immediately sometimes the innovator should wait for a time before beginning the cycles the optimal solution exhibits strong state dependency with so called skiba curves separating regions in state space where various of these strategies are optimal there are even instances of intersecting skiba curves in most cases analytical expressions can be stated that characterize these skiba curves

optimal hedge ratio under a subjective re weighting of the original measure abstractin this article we study a risk minimizing hedge ratio with futures contracts where the risk of the hedged portfolio is measured through a spectral risk measure srm thus incorporating the degree of agent s risk aversion we empirically estimate the optimal hedge ratio ohr using a long time series of uk and us equity indices the eurusd and eurgbp exchange rates and four liquid commodities brent crude oil corn gold and copper to represent different asset classes comparing the results with common ohrs such as the minimum variance and the minimum expected shortfall we find that the agent s risk aversion has a material impact and should not be ignored in risk management

a generalized model of operations reversal for fashion goods operations reversal is a process design principle that involves switching two consecutive stages of the manufacturing process to improve process performance in this paper we investigate conditions under which operations reversal can be used to reduce the variability as measured by the variance and standard deviation of production volumes at the intermediate stage of the manufacturing process we generalize the operations reversal model of lee and tang 1998 to explicitly incorporate two important characteristics of fashion goods markets heterogeneity among customers and unpredictability of customer preferences we also present a new approach to modeling the operations reversal problem

a comparison of var and cvar constraints on portfolio selection with the mean variance model in this paper we analyze the portfolio selection implications arising from imposing a value at risk var constraint on the mean variance model and compare them with those arising from the imposition of a conditional value at risk cvar constraint we show that for a given confidence level a cvar constraint is tighter than a var constraint if the cvar and var bounds coincide consequently a cvar constraint is more effective than a var constraint as a tool to control slightly risk averse agents but in the absence of a risk free security has a perverse effect in that it is more likely to force highly risk averse agents to select portfolios with larger standard deviations however when the cvar bound is appropriately larger than the var bound or when a risk free security is present a cvar constraint dominates a var constraint as a risk management tool

fashion and business cycles with snobs and bandwagoners in a multi sector growth model this paper generalizes the dynamic growth model with interactions between fashion economic growth and income and wealth distribution recently built by zhang 2016 the modelling of fashion and preference change is inspirited by the economic model of fashion recently published by giovinazzo and naimzada 2015 this study introduces fashion into neoclassical growth theory the original model is based on some ideas in the literature of economics of fashion this study generalizes zhang s model by making all the time independent parameters as time dependent parameters we simulate the motion of the economic system we carry out comparative dynamic analysis with regard to periodic perturbations in some parameters we show how exogenous period changes in these parameters lead to business cycles

structural analysis of optimal investment for firms with non concave revenue abstract qualitative properties of optimal investment strategies for a firm with quadratic costs that faces network externalities in its revenues are analysed organising the qualitative information in a bifurcation diagram it is found that the structure of the bifurcation manifolds is determined by a so called swallow tail singularity this implies the existence of up to three saddle equilibria of the state costate system whose local optimal stability for positive discount rates is determined by a three dimensional bifurcation diagram taking a particular two dimensional section of this diagram it is shown that the bifurcation curves divide this into 19 different parameter regions within each region the corresponding phase systems and also the optimal solutions derived from them are structurally stable in particular stable configurations with threshold skiba points are found in this way

economic implications of using a mean var model for portfolio selection a comparison with mean variance analysis abstract we relate value at risk var to mean variance analysis and examine the economic implications of using a mean var model for portfolio selection when comparing two mean variance efficient portfolios the higher variance portfolio might have less var consequently an efficient portfolio that globally minimizes var may not exist surprisingly we show that it is plausible for certain risk averse agents to end up selecting portfolios with larger standard deviations if they switch from using variance to var as a measure of risk therefore regulators should be aware that var is not an unqualified improvement over variance as a measure of risk

the economic value of controlling for large losses in portfolio selection abstract research on asset pricing has shown that investor preferences include asymmetry and tail heaviness which affects the composition of optimal portfolios this article investigates the out of sample economic value of introducing the risk of very large losses in portfolio selection we combine mean variance analysis with conditional value at risk using the subadditivity property of conditional value at risk and we introduce a two stage method that preserves diversification while controlling for large losses we find that strategies that account both for variance and the probability of large losses outperform efficient mean variance portfolios during and after the global financial crisis

behavioural heterogeneity under evolutionary pressure macroeconomic implications of costly optimisation a model is developed in which a continuum of agents makes interdependent output decisions in a stochastic environment characterised by strategic complementarity two groups are distinguished naive agents follow a costless adaptive expectations rule while sophisticated agents incur an optimisation cost to achieve self fulfilling expectations the paper studies the dynamics generated as the population composition evolves under pressure of differential payoffs sophisticated agents are favoured if optimisation is cheap or the stochastic environment highly variable but naive agents generally persist a higher long run share of sophisticated agents is associated with greater output variability and low output persistence several attempts have been made in the recent macroeconomic literature to explore the implications of allowing for behavioural heterogeneity among economic agents typically the standard postulates of unbounded rationality are held to apply only to a subset of the population while the remainder is assumed to behave in accordance with some alternative specification the nature of which depends on the situation being analysed akerlof and yellen

shortfall as a risk measure properties optimization and applications motivated from second order stochastic dominance we introduce a risk measure that we call shortfall we examine shortfall s properties and discuss its relation to such commonly used risk measures as standard deviation var lower partial moments and coherent risk measures we show that the mean shortfall optimization problem unlike mean var can be solved e7ciently as a convex optimization problem while the sample mean shortfall portfolio optimization problem can be solved very e7ciently as a linear optimization problem we provide empirical evidence a in asset allocation and b in a problem of tracking an index using only a limited number of assets that the mean shortfall approach might have advantages over mean variance 2003 elsevier b v all rights reserved

the optimal portfolio problem with coherent risk measure constraints one of the basic problems of applied finance is the optimal selection of stocks with the aim of maximizing future returns and constraining risks by an appropriate measure here the problem is formulated by finding the portfolio that maximizes the expected return with risks constrained by the worst conditional expectation this model is a straightforward extension of the classic markovitz mean variance approach where the original risk measure variance is replaced by the worst conditional expectation the worst conditional expectation with a threshold a of a risk x in brief wcea x is a function that belongs to the class of coherent risk measures these are measures that satisfy a set of properties such as subadditivity and monotonicity that are introduced to prevent some of the drawbacks that affect some other common measures this paper shows that the optimal portfolio selection problem can be formulated as a linear programming instance but with an exponential number of constraints it can be solved efficiently by an appropriate generation constraint subroutine so that only a small number of inequalities are actually needed this method is applied to the optimal selection of stocks in the italian financial market and some computational results suggest that the optimal portfolios are better than the market index 2003 elsevier b v all rights reserved

beyond expected utility subjective risk aversion and optimal portfolio choice under convex shortfall risk measures abstract we conduct a decision theoretic analysis of convex shortfall risk measures regarding their flexibility to represent subjective risk aversion and discuss the implications for the choice of optimal portfolios as convex shortfall risk measures are closely related to the expected utility functional we draw upon the expected utility framework as our benchmark first we show that unlike expected utility convex shortfall risk measures do always represent constant absolute risk aversion this constitutes a significant limitation when changing initial wealth of e g investors is relevant interestingly though it is exactly this limitation that provides additional degrees of freedom in representing subjective risk aversion beyond expected utility when initial wealth is fixed as e g in returned based portfolio selection models in the tradition of markowitz 1952 second we apply convex shortfall risk measures to the standard portfolio problem between a riskless and a risky asset we provide a procedure that allows inferring the optimal portfolios under convex shortfall risk measures from certain optimal expected utility portfolios the procedure incorporates the additional degrees of freedom in modeling subjective risk aversion and thus allows more flexible and realistic portfolios compared to expected utility third we address the optimal portfolio choice between a riskless and a risky asset in the presence of an additional background risk again we prove a correspondence result between optimal portfolios under convex shortfall risk measures and expected utility and obtain more flexible and realistic portfolios compared to expected utility we also compare the optimal risky investments without and with background risk and provide a necessary and sufficient condition for a reduction of the risky investment

efficient supply contracts for fashion goods with forecast updating and two production modes we examine the problem of developing supply contracts that encourage proper coordination of forecast information and production decisions between a manufacturer and distributor of high fashion seasonal products operating in a two mode production environment the first production mode is relatively cheap but requires a long lead time while the second is expensive but offers quick turnaround we focus on contracts of the form w1 w2 b wherewi is the wholesale price offered for production modei andb is a return price offered for items left over at the end of the season we find that such a contract can coordinate the manufacturer and distributor to act in the best interest of the channel the pricing conditions needed to ensure an efficient solution vary depending on the degree of demand forecast improvement between periods and the manufacturer s access to forecast information we also examine whether these conditions ensure a pareto optimal solution with respect to two traditional production settings

expected shortfall spectral risk measures and the aggravating effect of background risk or risk vulnerability and the problem of subadditivity abstract we analyze spectral risk measures srms including its most popular representative expected shortfall es with respect to gollier and pratt 1996 s concept of risk vulnerability we find that srms and risk vulnerability are mutually exclusive owing to the property of subadditivity while subadditivity is commonly regarded as the axiomatic cornerstone of srms risk vulnerability by contrast prevails if and only if superadditivity holds the lack of risk vulnerability yields questionable predictions in portfolio problems srm decision makers who split their wealth between a risk free and a risky asset do constantly opt for an increase in the risky investment when their deterministic background wealth is complemented by some additional background risk the more general setting where background wealth is already random and then becomes more risky is not as clear cut any srm decision maker may both increase or decrease the risky investment depending on the concrete instance of the portfolio problem however when random background wealth and the risky asset are jointly normally distributed srm decision makers will again unambiguously increase their risky investment we further conduct a data analysis and discuss possible implications of the findings for regulatory risk management

optimal pricing of a conspicuous product during a recession that freezes capital markets abstract this paper considers the problem of how to price a conspicuous product when the economy is in a recession that disrupts capital markets a conspicuous product in this context is a luxury good for which demand is increasing in brand image brand image here means the ability of a consumer to impress observers by conspicuously displaying consumption of the good brand image is built up when the good is priced high enough to make it exclusive and eroded if the good is discounted recession is modeled as having two effects it reduces demand and it freezes capital markets so borrowing is not possible in pricing the conspicuous product the firm faces the following trade off reducing price helps maintain sales volume and cash flow in the face of reduced demand but it also damages brand image and thus long term demand the paper analyzes the firm s pricing policy facing scenarios of mild intermediate and severe recessions while taking the threat of bankruptcy into account for an intermediate recession the optimal solution is history dependent the results have implications for policy interventions in capital markets and for timing of mergers and acquisitions

a dns curve in a two state capital accumulation model a numerical analysis abstract in this paper we study a capital accumulation model in an optimal control theoretic framework where the capital stock and the investment rate are modelled as state variables and the change in the investment rate as control adjustment costs are introduced for investment rate and its change moreover we model network externalities by a convex segment in the revenue function which implies the existence of two long run optimal steady states one with a low level and the other with a high level capital stock it depends on the initial capital endowment and initial investment rate to which steady state it is optimal to converge we numerically compute a curve in the state plane for which it holds that when starting from a point on this curve the decision maker is indifferent between going to either one of these steady states and identify this curve as the dns curve the negative slope of the dns curve indicates that there is a trade off between the initial capital endowment and initial investment rate

toward an economic theory of fashion strong as is the desire for variety it is weak compared with the desire for distinction a feeling which if we consider its universality and its constancy that it affects all men at all times that it comes with us from the cradle and never leaves us until we go to the grave may be pronounced to be the most powerful of human passions nassau senior 1 with the greater part of rich people the chief enjoyment of riches consists in the parade of riches which in their eyes is never so complete as when they appear to possess those decisive marks of opulence which nobody can possess but themselves adam smith 2 i introduction positively sloped demand curves are used in marketing textbooks to explain the pricing of fashion merchandise 3 snob or prestige effects are alluded to in support of the claim that price increases can lead to an increase in the quantity demanded in the tenth edition of their text e jerome mccarthy and william d perreault 1990 offer a demand curve with a positively sloped segment they explain prestige pricing is setting a rather high price to suggest high quality or high status some target customers want the best so they will buy at a high price but if the price seems cheap they worry about quality and don t buy p 506 footnote omitted emphasis in the original in another text ralph m gaedeke and dennis tootelian 1983 also discuss a positively sloped demand curve some products do not have the traditional downward sloping demand curve previously described but a more curved slope illustrated in exhibit 13 6 demand curve with upward sloping portion not shown this reflects the real impact of price as a part of the product s value quite obviously as a product s price rises above p sub 0 demand will begin to drop as some consumers will simply be unable to afford the product however that decline is rather slow until very high prices are reached but demand also begins to drop at prices below p sub 0 showing that part of the reason for owning the product lies in its high price it has prestige value economists react by asserting that marketing explanations are ad hoc devoid of economic content conversely marketers say that economic models are naive and incapable of explaining the marketing of fashion goods as economists we have a bias towards economic explanations but these explanations are incomplete and not highly valued by the market in stark contrast the advice of professional marketers that economists contend is muddled or worse is amply rewarded in consulting work is there a market failure in the consulting market or does marketing provide an insight that economics lacks we start with the premise that the intuition behind marketing explanations that people desire prestige has validity this notion can be incorporated into economic theory using kelvin lancaster s 1971 notion that when a purchase is made what is bought is a bundle of services or characteristics the salient feature of a fashion good is its ability to confer prestige or status 4 the argument is straightforward there is a sociobiological basis for status seeking behavior status seeking is an evolved trait that is innate to humans as well as to many other animals given the pervasiveness of status seeking human cultures have developed effective signals of status fashion being just one we incorporate the status yielding nature of fashion goods into a standard demand model by assuming that the value consumers attach to a fashion good depends on the stock held by other consumers this interdependency among consumers allows us to explain the upward sloping constructs labeled demand curves that populate marketing texts our model has downward sloping demand curves throughout but because of the interdependencies generates cyclical price behavior that can be misconstrued as aberrant positively sloped demand functions

novelty preferences and fashion when goods are unsettling abstract there is a whole class of goods those semi durable and durable conveniences for which efficiency and functionality seem not to be the main characteristics of appeal but rather the variability they display in their design properties and in their connections with other goods these goods have not been much dealt with in economics yet these are the goods whose new variants households seem to consume in numbers to which consumers become addicted and in which fashions appear and disappear in this paper i offer a framework for understanding these phenomena without having to resort to one or another form of irrationality on the part of consumers the rationality i suggest however has to include also the cognitive and affective problems that arise when novelty appears

design innovation and fashion cycles a model of fashion cycles is developed in which designs are used as a signaling device in a dating game a monopolist periodically creates a new design over time the price of the design falls as it spreads across the population once sufficiently many consumers own the design it is profitable to create a new design and thereby render the old design obsolete this paper gives conditions under which all consumers would be better off by banning the use of fashion competition among designers may lead to less frequent changes in fashion and to higher prices than monopoly copyright 1995 by american economic association

poverty trap and global indeterminacy in a growth model with open access natural resources abstract in this paper we use global analysis techniques to analyze an economic growth model with environmental negative externalities giving rise to a three dimensional dynamic system the framework is the one introduced by wirl 1997 53 the dynamics of our model admits a locally attracting stationary state p 1 which is in fact a poverty trap coexisting with another stationary state p 2 possessing saddle point stability global dynamical analysis shows that under some conditions on the parameters if the initial values of the state variables are close enough to the coordinates of p 1 then there exists a continuum of equilibrium trajectories approaching p 1 and one trajectory approaching p 2 therefore our model exhibits global indeterminacy since either p 1 or p 2 can be selected according to agent expectations moreover we prove that conditions guaranteeing the attractivity of p 1 also imply the saddle point stability of p 2 however when p 1 is not attractive numerical simulations show the possible existence of one or two limit cycles an attractive one surrounding p 1 and one endowed with a two dimensional stable manifold surrounding p 2

capital stock management during a recession that freezes credit markets abstract this paper considers the problem of how to price a conspicuous product while maintaining liquidity during a recession which both reduces demand and freezes credit markets reducing price would help maintain cash flow but low prices can erode brand image and hence long term sales the paper extends earlier work of the same authors by explicitly deriving a firm s optimal cash management behavior taking into account that a too low cash level results in bankruptcy there are different sets of initial conditions for which qualitatively different solution trajectories are optimal we distinguish mild and severe recessions with mild recessions bankruptcy can be avoided for sure when the brand image is large enough in case the recession is of intermediate strength it can be optimal to throttle forward then back how aggressively one spends down cash reserves with the associated state constraint alternately being non binding binding non binding then binding in such a way that the firm ceases operation

conditional value at risk spectral risk measures and non diversification in portfolio selection problems a comparison with mean variance analysis abstract we study portfolio selection under conditional value at risk and as its natural extension spectral risk measures and compare it with traditional mean variance analysis unlike the previous literature that considers an investor s mean spectral risk preferences for the choice of optimal portfolios only implicitly we explicitly model these preferences in the form of a so called spectral utility function within this more general framework spectral risk measures tend towards corner solutions if a risk free asset exists diversification is never optimal similarly without a risk free asset only limited diversification is obtained the reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward risk tradeoff underlying the mean variance framework

veblen effects in a theory of conspicuous consumption the authors examine conditions under which veblen effects arise from the desire to achieve social status by signaling wealth through conspicuous consumption while veblen effects cannot ordinarily arise when preferences satisfy a single crossing property they may emerge when this property fails in that case budget brands are priced at marginal cost while luxury brands though not intrinsically superior are sold at higher prices to consumers seeking to advertise wealth luxury brands earn strictly positive profits under conditions that would with standard formulations of preferences yield marginal cost pricing the authors explore factors that induce veblen effects and they investigate policy implications copyright 1996 by american economic association

optimal control of interacting systems with dnss property the case of illicit drug use abstract in this paper we generalize a one dimensional optimal control problem with dnss property to a two dimensional optimal control problem this is done by taking the direct product of the model with itself i e we combine two similar system dynamics under a joint objective functional that is separable in both states and controls this framework can be applied to the construction of various optimal control problems such as optimal marketing of related products optimal growth of separate but interacting economies or optimal control of two related capital stocks we study such a system for a particular case drawn from the domain of drug control the main result of this paper is that in this domain even a modest amount of interaction can sometimes make a very big difference hence drawing conclusions by simplifying the real world into two independent one dimensional models may be problematic methodologically the combination of two systems with dnss property leads to a fascinating series of situations with multiple optimal steady states and associated threshold behavior these instances reflect some important recent developments in optimal dynamic control theory

decision making with expected shortfall and spectral risk measures the problem of comparative risk aversion abstract we analyze spectral risk measures with respect to comparative risk aversion following arrow 1965 and pratt 1964 for deterministic wealth and ross 1981 for stochastic wealth we argue that the arrow pratt concept per se well matches with economic intuition in standard financial decision problems such as willingness to pay for insurance and simple portfolio problems different from the literature we find that the widely applied spectral arrow pratt measure is not a consistent measure of arrow pratt risk aversion instead the difference between the antiderivatives of the corresponding risk spectra is valid within the framework of ross we show that the popular subclasses of expected shortfall and exponential and power spectral risk measures cannot be completely ordered with respect to ross risk aversion thus for all these subclasses the concept of ross risk aversion is not generally compatible with arrow pratt risk aversion but induces counter intuitive comparative statics of its own compatibility can be achieved if asset returns are jointly normally distributed the general lesson is that these restrictions have to be considered before spectral risk measures can be applied for the purpose of optimal decision making and regulatory issues