Dynamic advertising and pricing with constant demand elasticities

In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.     

Commitment, advertising and efficiency of two-sided investment in competitive search equilibrium

Competitive search entails both commitment to and advertising of pay-off relevant aspects of market participants. This paper considers incrementally the implications of each in a labor market where both workers and firms invest prior to market entry. A wide range of institutional arrangements are addressed within the same general framework. When the characteristics of jobs or workers are advertised the efficient outcome pertains. Commitment without advertising typically leads to market unravelling: the Diamond paradox. But, whenever wages and human capital are advertised, firms become residual claimants; the private and social returns to investment coincide. Absent wage commitment, the Hosios condition implies efficiency when investments are advertised.     

The no-arbitrage condition and financial markets with heterogeneous information

This paper examines the role of the no-arbitrage condition in financial markets with heterogeneous expectations. We consider a single-period, state-contingent claims model, withM risky securities andS states. There exist two types of heterogeneously informed investors, where the information heterogeneity is defined with respect to either the security payoff matrix, the state probability vector, or state partitions. When the information heterogeneity is defined with respect to either the security payoff matrix or state partitions, the no-arbitrage condition imposes a constraint on the dispersion of information between informed and uninformed investors. Further, the no-arbitrage condition is useful in ascertaining the patterns of heterogeneity among investors that are consistent with equilibrium. However, when the information heterogeneity is defined with respect to state probabilities, the role of the no-arbitrage condition is severely restricted. Finally, the no-arbitrage condition may have important implications for the (necessary and sufficient) conditions for the existence of an equilibrium price vector in financial markets with heterogeneous expectations.     

Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk

According to the classic no arbitrage theory of asset pricing, in a frictionless market a No Free Lunch dynamic price process associated with any essentially bounded asset is a martingale under an equivalent probability measure. However, real financial markets are not frictionless. We introduce an axiomatic approach of Time Consistent Pricing Procedure (TCPP), in a model free setting, to assign to every financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. We prove that the No Free Lunch condition for a TCPP is equivalent to the existence of an equivalent probability measure R that transforms a process between the bid price process and the ask price process of every financial instrument into a martingale. Furthermore we prove that the ask (resp. bid) price process associated with every financial instrument is then a R super-martingale (resp. R sub-martingale) which has a càdlàg version.     

Drivers of optimal prices in two-sided markets: the state of the art

In two-sided markets, a platform has two groups of customers and enables their interactions. Demand on one market side depends on demand on the other; therefore, when platforms set prices, they must consider this interdependency and set prices on both sides simultaneously. By surveying the vast theoretical marketing and economics literature, this article provides a clear and systematic overview of profit-maximizing pricing in two-sided markets. It identifies and structures the various drivers of those optimal prices. Using this framework, it summarizes the findings from prior research and offers an assessment of the state of the art with regard to drivers of optimal prices and their impacts on a platform’s price setting. This improves understanding of both the principles of two-sided markets and their optimal pricing. Finally, this state of the art paper suggests some directions for further research.     

Relative pricing of binary options in live soccer betting markets

Live soccer betting markets differ from other binary options markets in that all fundamental information is observable, the options mature in less than two hours and the markets are highly liquid. This study presents a new method for the identification of hidden information in market prices. The method is based on two independent Poisson distributions and on a numerical algorithm for the aggregation of all market price information into one rational number. The method is applied to an empirical dataset of real time market prices in 29,413 soccer games. The results indicate that the method selects the most profitable markets and allows for a significant improvement in average investment returns.     

Equilibrium pricing and advertising strategies for nondurable experience products in a dynamic duopoly

The quality of many consumer nondurable goods or services is sufficiently complex or obscure that consumers cannot completely verify the true quality in a single usage. For such ‘experience’ products or services, the accumulated consumer consumption experience of a brand is an important determinant of its sales or market share. The market share of a brand is in turn directly influenced by its own and the competitive price and advertising strategies, given the different levels of quality (among other factors). In this paper, we investigate the impact of the aggregate consumption experience on the firm's dynamic pricing and advertising strategies by developing a formal game-theoretic model of a dynamic duopoly. The model of competition does not yield explicit closed-form expressions for the dynamic price and advertising paths of the two firms. Hence, we simulate the equilibrium paths using a discrete-time algorithm. Our simulation results provide interesting insights into the dynamic equilibrium price and advertising paths, under a variety of realistic competitive scenarios.     

Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends

We investigate dynamical properties of a heterogeneous agent model with random dividends and further study the relationship between dynamical properties of the random model and those of the corresponding deterministic skeleton, which is obtained by setting the random dividends as their constant mean value. Based on our recent mathematical results, we prove the existence and stability of random fixed points as the perturbation intensity of random dividends is sufficiently small. Furthermore, we prove that the random fixed points converge almost surely to the corresponding fixed points of the deterministic skeleton as the perturbation intensity tends to zero. Moreover, simulations suggest similar behaviors in the case of more complicated attractors. Therefore, the corresponding deterministic skeleton is a good approximation of the random model with sufficiently small random perturbations of dividends. Given that dividends in real markets are generally very low, it is reasonable and significant to some extent to study the effects of heterogeneous agents’ behaviors on price fluctuations by the corresponding deterministic skeleton of the random model.     

Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty

This paper describes the first model considered in the computational suite project that compares different numerical algorithms. It is an incomplete markets economy with a continuum of agents and an inequality (borrowing) constraint.     

Liquidity and asset pricing: Evidence from the Chinese stock markets

We introduce a novel two-factor model, incorporating market and liquidity factors, which outperforms the CAPM and Fama–French factor models when applied to stock market returns in Shanghai and Shenzhen over 2000–2019. We compute the liquidity factor as the return on a liquidity-mimicking portfolio, which we construct simultaneously using two measures of liquidity (one of them capturing liquidity’s trading-quantity dimension, and the other associated with its price-impact dimension). Unlike the CAPM and Fama–French factor models, the advocated two-factor model is able to account for numerous return anomalies, such as size, book-to-market ratio, earnings-to-price ratio, cash-flow-to-price ratio, return-on-equity, and volatility. The model’s performance is similar when applied separately to the Shanghai and Shenzhen stock markets. Furthermore, it fares similarly over the 1994–2004 and 2005–2019 sub-periods. This result is somewhat surprising, because liquidity seems likely to have been substantially lower over 1994–2004, as the Chinese markets were noticeably smaller, and the critical market reform aimed at eliminating non-tradable shares by the end of 2006 did not occur until 2005.     

Asset pricing for inefficient markets: Evidence from China and India

Over last four decades, evidence of market inefficiencies has been widely documented by several scholars for all major stock markets in the globe. Chinese and Indian markets are not exempt. Inefficiencies in these markets are described by many authors as roots of all mispricing. Mispricing might be the outcome of application of familiar asset pricing models which may mislead an investor into adopting inappropriate policies for his new investments or for reallocating his old investments. In an alternative approach, we propose a transformation on original market returns in the objective of relaxing the strong assumption of market efficiency behind application of an asset pricing model. This modification will widen the scope of rational models on asset pricing ranging from an efficient to an inefficient market.     

Multibrand pricing as a strategy for consumer search obfuscation in online markets

This paper argues that a firm with multiple brands can obfuscate consumer search by excluding the brands of other firms from a consumer's consideration set. This is examined empirically by regressing price data for a leading U.K. motor insurance price comparison site (or “shopbot”). It finds that multibrand firms own three‐quarters of brands in this market, and that allowing for other brand strategies, they post significantly lower and clustered prices relative to other firms. The firms also conceal their brand ownership, consistent with search obfuscation. The results are not otherwise explained and they have implications for market competitiveness.     

Equilibrium in collateralized asset markets: Credit contractions and negative equity loans

We address a general equilibrium model with collateralized debt, credit contractions, and financial market segmentation. Restrictions on credit access make borrower’s optimal payment strategies–coupon payment, prepayment, and default–sensitive to idiosyncratic factors, even though the only payment enforcement is the seizure of collateral guarantees. We prove equilibrium existence, characterize optimal borrower’s payment strategies, and provide a numerical example illustrating our main results. A remarkable feature of our model is that it rationalizes the prevalence of negative equity non-recourse loans.     

Differential pricing and production strategies for heterogeneous products under cannibalization and promotional effects

This study examines the optimal pricing and production strategy of a closed-loop supply chain consisting of a manufacturer, a recycler, and consumers. Considering the cannibalization and promotion effects of remanufactured products on new and secondhand products, we constructed Stackelberg game models under different scenarios. We analyze the impact of the changes in the two effects on the optimal prices and production strategies of the manufacturer and recycler, as well as their countermeasures. We find that (i) how the cannibalization and promotional effects influence the manufacturer and the recycler's pricing and production strategies differ under different scenarios; (ii) when the two effects exceed a threshold, the manufacturer abandons new or remanufactured products, and the recycler prefers to stop production on its new products or continue to remanufacture products; and (iii) the two effects always reduce the profits of the manufacturer and increase the profits of the recycler.     

Matching, search and intermediation with two-sided heterogeneity

This paper analyzes the role played by intermediation in a decentralized market, where trade is carried out through bilateral bargaining, and where the bargaining outcome depends on the process of search for suitable trading partners. To this purpose, a monopolistic intermediary is embedded in a dynamic model of random-matching and two-sided search with heterogeneous agents. It is shown that intermediation might speed up the matching process and might induce separation of the agents’ types, thus enhancing sorting efficiency with respect to a pure search market, where sorting externalities cause multiplicity of equilibria to arise and determine inefficient matching outcomes. Nonetheless, intermediation might also introduce frictions that do not exist in a decentralized market operating in isolation, and this impairs efficiency.      

Price and quantity competition among heterogeneous suppliers with two-part pricing: applications to clubs, local public goods, networks, and growth controls

Models of club goods, local public goods, and growth controls appear to have theoretical structures distinct from usual oligopoly models. This article shows, however, that they are special cases of a generalized oligopoly model that incorporates the possibility of two-part pricing and externalities between consumers (either congestion or network externalities). Our generalized two-part pricing model not only serves as a synthesis of a wide range of models but also allows us to obtain several new results on equilibrium prices. Another advantage of our model is that it can be interpreted as a reduced form of more complicated models that have spatial structures. This facilitates extension to the case where firms are heterogeneous and the number of firms is arbitrary.     

Disagreement with procyclical beliefs and asset pricing

We consider a pure exchange economy with incomplete information in which the expected growth rate of endowment is unobservable. The economy is populated by two investors, one is rational, but the other irrationally believes that the dynamics of endowment exhibit procyclical feature. Such different opinions about the dynamics of endowment process produce persistent disagreement between the investors. We show that model-implied riskfree rate is procyclical. Further, the procyclical beliefs not only explain the excess volatility puzzle, but also help to explain the mixed results about the relationship between the investors’ belief dispersions and stock return. Moreover, we uncover that the rational investor prefers to short stock positions in good times as the degree of the other investor’s irrationality increasing.     

Heterogenous beliefs with sentiments and asset pricing

We present a dynamic equilibrium model with two irrational investors: an extrapolator and a contrarian, whose beliefs regarding the growth rate of dividend stream are biased by their sentiments. The key contribution is to connect two disagreements with the degree of irrationality of investors and to provide novel insights into the predictability of stock return. We show that the higher level of sentiment disagreement is, the more stock price is overvalued. However, the future stock price will decline because the extrapolator’s sentiment will cool down over time. Therefore, the sentiment disagreement negatively predicts future return. At the meanwhile, our model not only shows that the survey expectations about cashflows increase the variations in asset price and dampen the corresponding volatility, but also helps to explain the mixed results about the relationship between the investors’ belief dispersions and stock return predictability.     

Disagreements with noisy signals and asset pricing

We consider a Lucas-type exchange economy with two trees and two investors to analyze the effects of heterogeneous beliefs and signal quality on stock market equilibrium. Our model has the following implications. There are spillover effects, in that the investors’ heterogeneous beliefs and signal quality related to one stock not only affect its own price and pricing moments, but also affect those of the other. Contrary to the conventional wisdom, we show that the volatility of one stock decreases with both its own and the other stock’s disagreements. Additionally, we reveal a negative correlation between the stocks, which decreases as the investors’ dispersions raise but increases as the discrepancy in signal quality reduces. We also show that heterogeneous beliefs and signal quality impact stock market beta mainly through scale and volatility effects, respectively. Furthermore, our findings suggest that both heterogeneous beliefs and signal quality have significant influences on the investors’ optimal portfolio plans.