INDIFFERENCE PRICES AND IMPLIED VOLATILITIES

We consider a general local‐stochastic volatility model and an investor with exponential utility. For a European‐style contingent claim, whose payoff may depend on either a traded or nontraded asset, we derive an explicit approximation for both the buyer's and seller's indifference prices. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surfaces. For European claims on a nontraded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.     

Why offer lower prices to past customers? Inducing favorable social price comparisons to enhance customer retention

Price discrimination policies vary widely across companies. Some firms offer new customers the lowest price; others give preferential prices to their past customers. We contribute to the literature on price discrimination in behavior-based pricing by exploring how customers’ social price comparisons, i.e., comparing one’s price to that received by similar peers, impact the optimal structure of price discrimination. Social price comparisons have a negative (positive) impact on customers’ transaction utility if the price charged to past customers is higher (lower) than a new customer’s price. Using an analytical model with vertically differentiated firms, we show that a firm with relatively large market share will reward its past customers with relatively low prices when social price comparisons have a sufficiently large impact on utility. Furthermore, we find that social price comparisons lead to a relaxation of the price competition for new customers. Thus, both firms can earn higher profits when such comparisons are made than when they are absent. We also examine how other factors, such as horizontal competition and strategic customers, interact with social price comparison concerns to impact pricing strategies. Finally, we show how pricing behavior differs when price comparisons are based on historic reference prices rather than on peers’ prices.     

An Empirical Analysis of Bidding Fees in Name-your-own-price Auctions

Interactive pricing mechanisms integrate customers into the price-setting process by letting them submit bids. Name-your-own-price auctions are such an interactive pricing mechanism, where buyers' bids denote the final price of a product or service in case they surpass a secret threshold price set by the seller. If buyers are given the flexibility to bid repeatedly, they might try to incrementally bid up to the threshold. In this case, charging fees for the option to place additional bids could generate extra revenue and reduce incremental bidding behavior. Based on an economic model of consumer bidding behavior in name-your-own-price auctions and two empirical studies, we analytically and empirically investigate the effects bidding fees have on buyers' bidding behavior. Moreover, we analyze the impact of bidding fees on seller revenue and profit based on our empirical results.     

自主创新激励下企业政府采购最优出价行为研究

在政府采购过程中,促进自主创新的政策与公开招标经济目标之间存在着一定冲突。本文在一价密封模型的基础上,通过改变供应商的效用函数,考察了政府鼓励自主创新条件下企业（供应商）的最优报价。结果表明：政府扶持自主创新的政策会改变供应商的出价机制,获得优惠较多的供应商会提高报价,并且随着竞标人数的增多最优价格将接近中标企业的成本。     

Strategic Bidding for Multiple Units in Simultaneous and Sequential Auctions

A buyer in an electronic marketplace may be interested in buying a bundle of items, where any one item in the bundle may not be of particular interest. The emergence of online auctions allow such users to obtain bundles by bidding on different simultaneous or sequentially run auctions. Because the number of auctions and the number of combinations to form the bundles may be large, the bundle bidding problem becomes intractable and the user is likely to make sub-optimal decision given time constraints and information overload. We believe that an automated agent that takes user preferences and budgetary constraints and can strategically bid on behalf of a user can significantly enhance user profit and satisfaction. Our first step to developing such an agent is to consider bundles containing many units of a single item to be bought from auctions that sell only multiple units of one item type. We assume that users obtain goods over several days. Expectations of auctions and their outcome in the future allow the agent to bid strategically on currently open auctions. We present an expected utility based strategy to decide how many items to bid for in the current auctions, and the maximum price to bid for each item. We evaluate our proposed strategy in different configurations by varying the number of items sold per auction, number of concurrently running auctions, expected closing prices, etc. We simulate several multiple unit English auctions per day, over multiple days, where most of the bidders bid their true utilities drawn from a distribution. The strategic bidding agent has knowledge of this distribution and uses it to determine its bids. A strategic agent who looks farther ahead into the future produces larger returns when there are few strategic bidders. We also evaluate the effect of risk attitudes on the relative performance of the bidders.     

The impact of household level heterogeneity in reference price effects on optimal retailer pricing policies

The field of marketing has witnessed substantial improvement in modeling household level heterogeneity. However, relatively little has been written about how modeling household heterogeneity translates into better marketing decisions. In this paper, we study the impact of household level heterogeneity in reference price effects on a retailer's pricing policy. Reference prices are certain anchors or standards that households use to compare the observed purchase price of a product against. If the observed price is greater than the reference price it is perceived as a “loss” and if it is smaller than the reference price it is perceived as a “gain”. In order to study the impact of heterogeneity in reference price effects on retail pricing, we test a nested logit model under two alternative reference price (memory and stimulus based) and heterogeneity (finite mixture and hierarchical Bayes) specifications. In the empirical analysis, we find that households are quite heterogeneous in terms of their gain and loss effects. For some households a gain has higher impact than a corresponding loss, while the opposite is true for others. Using individual level estimates we then develop a normative pricing policy for a retailer maximizing category profit. Our results indicate that the optimal pricing policy derived from the heterogeneous case is qualitatively different, and more profitable, than the case when heterogeneity is ignored. We show that for an important marketing problem pertaining to a retailer, the optimal pricing decisions for various brands in a category are inextricably related to household heterogeneity in reference effects and brand preference.     

MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.     

Arbitrage‐free XVA

We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no‐arbitrage arguments, we derive backward stochastic differential equations associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no‐arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the unique XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. In the general case of asymmetric funding, repo, and collateral rates, we study the semilinear partial differential equations characterizing buyer's and seller's XVA and show the existence of a unique classical solution to it. To illustrate our results, we conduct a numerical study demonstrating how funding costs, repo rates, and counterparty risk contribute to determine the total valuation adjustment.     

Optimal pricing in social networks considering reference price effect

We study the optimal monopoly pricing strategies in a social network, in which consumers experience a network effect that is dependent on their neighbors' consumptions and a reference price which is the average price received by their neighbors. We establish a two-stage game model for any social network. Utilizing the backward induction, we derive the equilibrium price by maximizing the monopolist's profit. In addition, we apply this model to the two most commonly used network structures: the star network and the bipartite network. We find that both the network effect and the reference price effect play a critical role in deciding pricing strategies in social networks. Moreover, our numerical results demonstrate that whether to implement discriminatory pricing depends critically on the network structure. This work provides monopoly firms a useful guideline for optimal pricing decisions in social network marketing.     

Anchoring Induced Biases in Consumer Price Negotiations

Two studies were conducted with the aim of demonstrating anchoring induced biases in consumer price negotiations.In Study 1, 96 undergraduate students of business administration who were recruited as subjects played the role of buyers of a condominium. All subjects were given the same market information. They were then asked to state whether their reservation price was higher or lower than an arbitrary price example (irrelevant anchor) that for different groups of subjects was either low or high. Finally, subjects indicated their reservation price. As would be predicted if adjustments from the anchor are insufficient, the indicated reservation price was lower when the anchor was low than when it was high.In Study 2, employing 64 undergraduate students of psychology who conducted dyad negotiations about the price of condominiums, the effect of the irrelevant anchor on the initially indicated reservation price was replicated. In addition, an anchoring effect of the seller's initial offer was observed. The results also revealed effects of both irrelevant anchor and initial offer on the purchase price.From a public policy point of view, the results imply that consumers may be strongly influenced by irrelevant anchors provided by sellers. Provision of accurate market price information may however lessen the impact of irrelevant anchors.     

An Extension of Ausubel's Auction for Heterogeneous Discrete Goods

Ausubel's dynamic private‐values auction for heterogeneous discrete goods, Ausubel (2006), yields an efficient equilibrium outcome but it is designed for a limited class of environments. If bidders’ values for bundles of goods are not integers, then Ausubel's auction may end without allocating goods if no information on bidders’ values is available. In this paper, I extend Ausubel's auction for heterogeneous discrete goods to real‐valued quasilinear utility functions. The mechanism I propose reaches a Walrasian equilibrium price vector in finite ‘steps’ without any additional information on bidders’ values. In the extension of Ausubel's auction, truthful bidding constitutes an efficient equilibrium.     

Prior knowledge and the effect of suggested frames of reference in advertising

This research builds on framing and anchoring and adjustment research and proposes suggested frames of reference as a means to influence buyer behavior. Theory and hypotheses are tested in an experiment of video camera purchases. The empirical results suggest that response to suggested frames of reference varies, depending on the buyer's prior category knowledge. Low-knowledge buyers are influenced by price frames. High-knowledge buyers are influenced by outcome frames. Positive frames are more influential than negative frames. © 1997 John Wiley & Sons, Inc.     

Strategic Trade Policy through the Tax System

If conventional instruments of strategic trade policy are unavailable, the system of foreign profit taxation and transfer price guidelines may serve as surrogate policy instruments. In this paper, I consider a model where firms from two countries compete with each other on a market in a third country. Both firms have affiliates in the third country where (part of) the production takes place. I analyse optimal policy choices of the firms' residence countries aiming at strategically manipulating the competitiveness of their firms. I show that, first, countries prefer the tax exemption system over the tax credit system if there is no intra‐firm trade. Second, if the headquarters provide inputs for production in the affiliate, countries prefer the tax exemption system if the transfer price for these inputs is close to the headquarters' variable cost and if the residence country's tax rate is high. However, if transfer prices are high and the residence country's tax rate is low, I show that the tax credit system is an optimal tax policy choice for both countries. From a policy perspective, the view that the tax exemption system is generally the best policy response if domestic firms' competitiveness is a policy goal has to be qualified.     

Life-time income of men and women — the case in Denmark

Life-time income is estimated here including the money value of household work. A modified opportunity principle is used, which means that non-employed women's price of time is found by calculating reservation wage rates. The overall results demonstrate that Danish women's ‘loss' of labour income during the child caring period is difficult for them to regain, and just to reach the same level of income as childless Danish women seems impossible; furthermore Danish men get a higher life-time income than Danish women even when we add the money value of household work.     

On manufacturers complementing the traditional retail channel with a direct online channel

With the explosion of the Internet and the reach that it affords, many manufacturers have complemented their existing retail channels with an online channel, which allows them to sell directly to their consumers. Interestingly, there is a significant variation within product categories in manufacturer's use of the Internet as a direct distribution channel. The main objective of this study is to examine the strategic forces that may influence the manufacturer's decision to complement the retail channel with a direct online channel. In particular, we are interested in answering the following questions:

1. Why is it that in some markets only a few firms find it optimal to complement their retail channels with a direct Internet channel while other firms do not?
2. What strategic role (if any), does the direct Internet channel serve and how do market characteristics impact this role?

To address these issues we develop a model with a single strategic manufacturer serving a market through a single strategic retailer. In addition to the focal manufacturer's product the retailer carries products of competing manufacturers. Consumers in this market are one of two types. They are either brand loyal or store loyal. The retailer sets the retail price and the level of retail support, which impact the demand for the manufacturer's product. The retailer's decisions in turn depend on the wholesale price as well as the Internet price of the product if the manufacturer decides to complement the retail channel with an online channel. Our analysis reveals that the optimality of complementing the retail channel with an online channel and the role served by the latter depends critically upon the level of support that the retailer allocates to the manufacturer's product in the absence of the online channel. The level of support allocated by the retailer, in the absence of the online channel, depends upon the retail margins on the manufacturer's product relative to that on rival products in the product category. When the size of the brand loyal segment is small relative to the size of the store loyal segment then in the absence of the online channel, the manufacturer can lower wholesale price and enhance retail support, especially when the retail margins on the rival products are low. In contrast, when the size of the loyal segment is large and the retail margins on rival products are high the manufacturer will find it more profitable to charge a high wholesale price even if that induces the retailer to extend low levels of support. If the manufacturer decides to complement the retail channel with an online channel, some consumers who would have purchased from the retailer might prefer to purchase online. Our analysis reveals that when consumers' sensitivity to price differences across the competing channels exceeds a certain threshold it is not optimal for the manufacturer to complement the retail channel with an online channel. However, this price sensitivity threshold itself depends upon product/market characteristics, suggesting that manufacturers seeking to complement their retail channels with an online channel should look beyond the nature of threat the online channel poses to the retail channel in devising their optimal distribution strategies. When the retail margins on rival products are sufficiently small, complementing the retail channel with an online channel when optimal allows the manufacturer to price discriminate and enhance profits. In contrast when retail margins on rival products are sufficiently high, complementing the retail channel with an online channel serves to enhance retail support. We also identify market conditions under which profits of both the manufacturer and the retailer are greater with the online channel than that without it. This is particularly interesting since the online channel competes with the retail channel.     

Shortfall aversion

Shortfall aversion reflects the higher utility loss of spending cuts from a reference than the utility gain from similar spending increases. Inspired by Prospect Theory's loss aversion and the peak‐end rule, this paper posits a model of utility from spending scaled by past peak spending. In contrast to traditional models, which call for spending rates proportional to wealth, the optimal policy in this model implies a constant spending rate equal to the historical peak when wealth is relatively large. The spending rate increases when wealth reaches a model‐determined multiple of peak spending. In 1926–2015, shortfall‐averse spending is smooth and typically increasing.     

Performance Implications of a Retail Purchasing Network: The Role of Social Capital

This study employs social capital theory to examine how a retail buyer's network of industry peers influences retail performance. We propose that performance is enhanced by three network resources – access, referral, and influence – that result from two structural facets of a retail buyer's network: contact diversity and contact position. We test the model by collecting sociometric data that measures interpersonal ties among 84 retail buyers operating in the same geographic territory in the U.S. golf industry. The results offer evidence that network resources lead to higher levels of performance, even when accounting for differences in human capital and organizational resources. The paper concludes with a discussion of managerial and theoretical implications.     

VALUATION OF CLAIMS ON NONTRADED ASSETS USING UTILITY MAXIMIZATION

A topical problem is how to price and hedge claims on nontraded assets. A natural approach is to use for hedging purposes another similar asset or index which is traded. To model this situation, we introduce a second nontraded log Brownian asset into the well-known Merton investment model with power law and exponential utilities. The investor has an option on units of the nontraded asset and the question is how to price and hedge this random payoff. The presence of the second Brownian motion means that we are in the situation of incomplete markets. Employing utility maximization and duality methods we obtain a series approximation to the optimal hedge and reservation price using the power utility. The problem is simpler for the exponential utility, and in this case we derive an explicit representation for the price. Price and hedging strategy are computed for some example options and the results for the utilities are compared.     

Who Benefits from Workers with General Skills? Countervailing Incentives in Labour Contracts

In a principal–agent model with adverse selection and moral hazard the impact of the agent's transferable human capital on incentives is analysed. It is shown that under asymmetric information the employer (principal) prefers a worker (agent) with general skills to a similarly productive worker with firm‐specific skills although the reservation utility of a worker with general (i.e. marketable) skills is higher. The principal's information costs are lower when workers have general skills than in the case where workers possess only firm‐specific human capital because of countervailing incentives. The optimal contract for workers with general skills differs from the standard screening contract in that it involves pooling.     

Anchor Points, Reference Points, and Counteroffers in Negotiations

Based on the theoretical assumptions that counteroffers are generated through an anchoring-and-adjustment process and that offers are perceived as gains or losses relative to a reference point, predictions were made of how, in a price negotiation, the size of counteroffers vary with proposed selling prices and reservation prices. The predictions were confirmed in two experiments. In Experiment 1, 64 undergraduate students of business administration playing the role of buyers of condominiums were presented proposed selling prices and asked to give a counteroffer which a hypothetical seller would accept or reject. A reference point was induced by telling subjects their reservation price. Before giving a counteroffer subjects were asked to indicate whether it was higher or lower than an arbitrary anchor point. In four different groups of subjects, high vs. low reference point was crossed with high vs. low anchor point. The results showed as expected that the counteroffers were higher for a high than for a low anchor point, and higher for a high reference point when the anchor point was perceived as a gain than for a low reference point when the anchor point was perceived as a loss. In Experiment 2 in which another 48 undergraduate students of business administration participated, the anchor points were the proposed selling prices and the reference point (reservation price) was manipulated by providing estimates of the market price. The results were as predicted, thus suggesting that the proposed selling prices operated as anchor points and that the estimated market prices affected the reservation prices (reference points) so that the selling prices and estimated market prices jointly affected the counteroffers.