Linear Pricing Research Articles

Strategic Execution Trajectories

ABSTRACT We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact, however uniqueness in general remains unproven. Various numerical examples are included for illustration.

A Novel Contract Theory-Based Incentive Mechanism for Cooperative Task-Offloading in Electrical Vehicular Networks

The proliferation of compute-intensive services in next-generation vehicular networks will impose an unprecedented computation demand to meet stringent latency and resource requirements. Vehicular edge or fog computing has been a widely adopted solution to enhance the computational capacity of vehicular networks; however, the computation requirements of these compute hungry applications will surpass the capabilities of such a solution. To address this challenge, the on-board resources of neighboring mobile vehicles can be utilized. However, such resource utilization requires an incentive mechanism to motivate privately owned neighboring vehicles to participate in sharing their resources. In this paper, we propose a contract theory-based incentive mechanism that maximizes the social welfare of the vehicular networks by motivating neighboring vehicles to participate in sharing their resources. The proposed approach enables the Road Side Units (RSUs) to provide appropriate rewards by offering a tailored contract to each resource sharing vehicle based on their contribution and unique characteristics. Moreover, we derive an optimal contract scheme for computational task offloading, taking into account the individual rationality and incentive-compatible constraints. Finally, we perform numerical evaluations to demonstrate the effectiveness of our proposed scheme. The proposed scheme achieves up to 28% higher computing resource utilization, 17.2% lower energy consumption per computing resource utilization, and 17.1% lesser energy consumption per task completed when compared to the linear pricing incentive baseline.

Linear pricing game based power control with resource allocation and interference management in device‐to‐device communication for IoT applications

AbstractDevice‐to‐Device (D2D) communication is one of the leading technologies which works under the aegis of fifth generation (5G) communication for the Internet of Things in Healthcare. In D2D communication, power control with resource allocation is the most challenging area for the research to make them suitable for IoT devices. In the present work, power control with resource allocation is done by using the Linear pricing game power allocation method. First, a mathematical min‐function based problem is proposed whilst taking the interference, data rate and minimum power requirement as a constraint to ensure the resource and power allocation. In the next phase, a linear pricing game (LPG) method is utilized to propose the LPG power control with resource allocation (L‐PaRAG). Mathematical analysis and theorem ensure the minimum cost function with global stability for an optimal solution of the proposed problem. Numerical analysis and results show that the proposed algorithm gives the best results for power control and resource management whilst managing the interference to maintain the quality of services (QoS) in D2D communication. Optimized power can be utilized for the communication between the base station and D2D users, especially, during disaster management.

Double Markups, Information, and Vertical Mergers

In vertical contracting models with complete information and linear prices, double markups that arise between independent firms provide an efficiency rationale for vertical mergers since these eliminate double markups (EDM). However, the double markups vanish even without vertical integration if the firms are allowed to use two-part tariffs. Hence, the efficiency rationale for vertical mergers in models of complete information requires restrictions on the contracts that firms can use. In a sense, with complete information, two-part tariffs are simply too powerful. If instead one allows incomplete information and removes the restriction on contract forms, then vertical mergers continue to have an effect that is analogous to EDM, but they also have the potential to affect the overall efficiency of the market to the detriment of society. Consequently, the social surplus effects of vertical integration depend on the underlying market structure, and vertical mergers are, in and of themselves, neither good nor bad. We illustrate through an example that with incomplete information, the private benefits from vertical integration tend to be excessive; that is, vertical mergers remain profitable even when they are socially harmful.

On tree-structured linear and quantile regression-based asset pricing

PurposeThis study aims to introduce a tree-structured linear and quantile regression framework to the analysis and modeling of equity returns, within the context of asset pricing.Design/Methodology/ApproachThe approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The framework is applied on numerous U.S. asset pricing models, using alternative mimicking factor portfolios, frequency of data, market indices, and equity portfolios.FindingsThe findings reveal strong evidence that asset returns exhibit asymmetric effects and non- linear patterns to different common factors, but, more importantly, that there are multiple thresholds that create several partitions in the common factor space.Originality/ValueTo the best of the authors' knowledge, this paper is the first to explore and apply a tree-structured and quantile regression framework in an asset pricing context.

How to charge doctors and price medicines in a two-sided online healthcare platform with network externalities?

Platform business models are upending the value proposition of the companies in traditional industries, such as healthcare, through competitively pricing value-added services and products. In this study, we consider a unique, but important, on-demand two-sided service platform: a monopolistic online healthcare platform, which not only provides medical services to patients by connecting them with doctors, but also sells medical products to patients. A crucial operational decision for the platform is to set up a pricing scheme to encourage enough doctors and patients to participate on the platform. We consider two common pricing schemes in this study: fixed and linear pricing, in an empirically-grounded optimisation model that considers medicine pricing decisions together with network externalities. Our results show that the fixed pricing scheme almost always dominates the linear pricing scheme by providing the platform with higher expected profit. Our results also reveal the strong interdependence between the optimal doctor service pricing decision and optimal medicine pricing decision. However, these decisions are often made independently by different functional units of a firm, which could cause suboptimal platform financial performance. These results indicate the importance of pricing products and services in an integrated manner for maximising the profit of a product/service platform.

Social desirability of entry in a bilateral oligopoly—The implications of (non) sunk costs

We show the implications of sunk investments for social efficiency of downstream-entry in a bilateral oligopoly. The possibility of socially excessive entry increases as the percentage of non-sunk investments increases. If there are no sunk investments or bargaining for the input prices occurs before investments as in the “ex-ante bargaining”, entry is always socially excessive. These results hold under both two-part tariff and linear input pricing.

Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact

We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk functional over a class of absolutely continuous and signal-adaptive strategies. The stochastic control problem is solved by following a probabilistic and convex analytic approach. We show that the optimal trading strategy is given by a system of four coupled forward-backward SDEs, which can be solved explicitly. Our results reveal how the induced transient price distortion provides together with the predictive signal an additional predictor about future price changes. As a consequence, the optimal signal-adaptive trading rate trades off exploiting the predictive signal against incurring the transient displacement of the execution price from its unaffected level. This answers an open question from [C. A. Lehalle and E. Neuman, Finance Stoch., 23 (2019), pp. 275--311] as we show how to derive the unique optimal signal-adaptive liquidation strategy when price impact is not only temporary but also transient.

Charging more for priority via two-part tariff for accumulating priorities

We consider an unobservable M/G/1 queue with accumulating priorities and strategic customers who pay for priority accumulation rates. We show that when affine pricing is introduced, multiple equilibria may exist. This is in contrast to the standard linear pricing case where the equilibrium strategy is unique. Furthermore, a revenue-maximizing operator may generate more revenue under the optimal affine pricing than under linear pricing. In particular, we show that if the utilization level is not too high, no other combination of a priority scheme and pricing generates more revenue than the optimal affine pricing of accumulating priorities.

Pricing Policy in an Inventory Model with Green Level Dependent Demand for a Deteriorating Item

The goal of this research is to investigate an inventory model for degrading commodities with linear selling prices and nonlinear green level-dependent demand for an item. The pre-payment option with a one-time flat reduction on the product’s selling price is considered here. The governing differential equations are used to mathematically define the model and solve numerically to optimize the model’s average profit. After that, the model is tested using a numerical example, and sensitivity analyses are run to see how changing inventory factors affects the best strategy. The concavity of the objective function is shown graphically with the help of MATLAB software. Finally, some applications of this approach and future scopes are discussed.

Empirical Asset Pricing with Functional Factors

Abstract We propose a methodology to use functional factors in empirical asset pricing models. We establish conditions under which it is possible to recover linear beta pricing. The proposed estimation approach allows us to use high-dimensional functional curves, such as the term structure of interest rates or the implied volatility smile, as factors. This framework enables the estimation of functional factor loadings as well as risk premium parameters of factor models. We derive estimation algorithms and establish the asymptotic consistency and normality of the parameter estimates. In an empirical application, we show that the implied variance smile of the S&P500 is a potential pricing factor for momentum-sorted portfolios. In particular, a positive risk premium is earned by the convexity of the implied variance curve.

Piecewise Linear Price Function of a Differential Game with Simple Dynamics and Integral Terminal Price Functional

In this paper, we consider an antagonistic differential game of two persons with dynamics described by a differential equation with simple motions and an integral terminal payment functional. In this game, there exists a price function, which is a generalized (minimax or viscous) solution of the corresponding Hamilton–Jacobi equation. For the case where the terminal function and the Hamiltonian are piecewise linear and the dimension of the phase space is equal to 2, we propose a finite algorithm for the exact construction of the price function. The algorithm consists of the sequential solution of elementary problems arising in a certain order. The piecewise linear price function of a differential game is constructed by gluing piecewise linear solutions of elementary problems. Structural matrices are a convenient tool of representing such functions.

Exploiting complete linear descriptions for decentralized power market problems with integralities

It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.

Marketing Mix Analysis on Outpatient Satisfaction at Medan Haji General Hospital

Quality health services cannot escape the reality of the importance of maintaining patient satisfaction, including in handling complaints submitted by patients. Professional and good hospital services to patients will benefit the hospital and have an impact on the increasing number of patient visits for treatment at the hospital. The purpose of this study was to determine the relationship between the mix of pice, place, people and process with patient satisfaction at the hospital. General Hajj Medan. This study uses a quantitative method with a cross sectional design, with a sample of 74 respondents. This research uses a questionnaire.The research time is February-November 2021 as a follow-up to the end of the research. The analysis of this study used Univariate, Bivariate and Multivariate. The statistical test used is the chi square test and longistic regression. The results of the study regarding the effect of Price (P-value 0.002), Place (P-value 0.007), People (P-value 0.006), Process (P-value 0.002), based on binary linear regression test price, place, people and process are variables which affects the satisfaction of outpatients at the Medan Haji General Hospital. The conclusion in this study shows that there is a significant influence between linear price, place, people and process with outpatient satisfaction at the Medan Haji General Hospital. related to effective patient management), providing cost leeway for underprivileged patients, compiling an organizational structure according to duties and education as well as adjusting the hospital organizational structure to the type of Medan Haji Hospital.

Pricing Behaviour and Menu Costs in Multi‐product Firms

This paper investigates the micro‐foundations of pricing behaviour using monthly producer prices for Norwegian multi‐product firms. We find both infrequent and many small price changes together with a high degree of within‐firm synchronization. This points at fixed menu costs featuring scope economies, at additional linear and convex price adjustment costs, and at the presence of firm‐specific shocks. The structural estimates and a simulation support the view that in order to understand pricing behaviour and the effectiveness of monetary policy, the analysis of multi‐product firms and a richer price adjustment technology in the intermediate goods sector is valuable.

Market Share Contracts in B2B Procurement Settings with Heterogeneous User Preferences

Market share contracts, a form of loyalty discounts, where the discount is contingent on the buyer meeting or exceeding a target share of total procurement, are used in many business to business (B2B) settings. We study the impact of such contracts on demand allocation, prices, and welfare in a setting where a single central B2B buyer procures multiple units of a product on behalf of a set of users with heterogeneous preferences. We find that linear pricing creates a demand distortion, which goes away with the use of market share contracts. These contracts serve as strategic tools for vendors whose products are strongly preferred by a substantial fraction of the users in the buying organization to shift the locus of competition and extract away rents from weaker rivals, and sometimes from buyers. The impact of such contracts on the welfare of the buyers is therefore ambiguous, but when these contracts are used, the overall surplus goes up as disutility from demand distortion is avoided. While both quantity threshold contracts and two‐part tariffs can replicate the efficiency properties of market share contracts when demand is deterministic, they cannot guarantee the avoidance of demand distortion when buyer demand is uncertain.

Short Communication: Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact

Short Communication: Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact

Transmit Power Control Game With a Sum Power Constraint in Cell-Free Massive MIMO Downlink

We propose a transmit power control game, where we assume that distributed access points are rational, i.e., they will determine the transmit power to maximize their own utility functions. The utility function of each AP is defined as the estimated downlink sum-rate minus a linear price function of the transmit power. The existence of the Nash-equilibrium of the proposed game is analyzed. In order to find the optimal price value for efficient transmit power allocation, an iterative search algorithm is also proposed. Simulation results show that the average spectral efficiency of the proposed scheme is better than that of both the equal transmit power allocation and waterfilling-based power allocation.

On non-negative equity guarantee calculations with macroeconomic variables related to house prices

This article investigates the impact of macroeconomic fundamentals on the valuation of non-negative equity guarantee (NNEG) of equity release mortgages. The house price returns are modeled within the family of multiplicative volatility processes using a two-component GARCH-MIDAS model. The pricing framework is constructed based on a general exponential linear pricing kernel, and the risk-neutral dynamics are derived assuming an autoregressive structure for the macroeconomic variables. Our numerical results indicate that the addition of macroeconomic variables improves the predictive performance of the house price returns and have a significant effect on the NNEG valuation.

The value does not exist! A motivation for extremal analysis

<p style='text-indent:20px;'>Standard mathematical economics studies the production, exchange, and consumption of goods “<i>provided with units of measurement</i>,” as in physics, in order to be enumerated, quantified, added, etc. Therefore, “baskets of goods,” which should describe subsets of goods, are mathematically represented as commodity vectors of a vector space, linear combination of units of goods, evaluated by prices, which are linear numerical functions. Therefore, in this sense, mathematical economics is a branch of physics.</p><p style='text-indent:20px;'>However, economics, and many other domains of life sciences, investigate also what will be called <i>entities</i>, defining <i>elements deprived of units of measure</i>, which thus cannot be enumerated.</p><p style='text-indent:20px;'>(1) Denoting by <inline-formula><tex-math id="M1">\begin{document}$X$\end{document}</tex-math></inline-formula> the set of entities <inline-formula><tex-math id="M2">\begin{document}$x \in X$\end{document}</tex-math></inline-formula> <i>deprived of units of measurement</i>, a “basket of goods” is actually a <i>subset</i> <inline-formula><tex-math id="M3">\begin{document}$K \subset X$\end{document}</tex-math></inline-formula> of the set entities, i.e., an element of the “<i>hyperset</i>” <inline-formula><tex-math id="M4">\begin{document}${\cal{P}}(X)$\end{document}</tex-math></inline-formula>, the family of subsets of <inline-formula><tex-math id="M5">\begin{document}$X$\end{document}</tex-math></inline-formula>, and no longer a commodity vector of the vector space of commodities;</p><p style='text-indent:20px;'>(2) Entities can be “gathered” instead of being “added”;</p><p style='text-indent:20px;'>(3) Entities can still be evaluated by a <i>family</i> of functions <inline-formula><tex-math id="M6">\begin{document}$A: x \in X \mapsto A(x) \in \mathbb{R}$\end{document}</tex-math></inline-formula> regarded as a “valuators,” in lieu and place of linear “prices” evaluating the units of economic goods.</p><p style='text-indent:20px;'>(4) Subsets of entities can be evaluated by an “<i>interval of values</i>” <i>between two extremal ones</i>, the minimum and the maximum, instead of the sum of values of units of goods weighted by their quantities.</p><p style='text-indent:20px;'>Life sciences dealing with intertwined relations among many combinations of entities, hypersets offer metaphors of “Lamarckian complexity” that keeps us away from binary relations, graphs of functions, and set-valued maps, to focus our attention on “<i>multinary relations</i>” between families of hypersets. Even deprived of units of measurement, these “proletarian” entities still enjoy enough properties for this pauperization to be mathematically consistent.</p><p style='text-indent:20px;'>This is the object of this <i>extremal manifesto</i>: <i>in economics and other domains of life sciences, vector spaces should yield their imperial status of “state space” to hypersets and linear prices to hypervaluators</i>.</p><p style='text-indent:20px;'>We no longer have to add goods which can only be gathered, prices do not have to be linear, although it costs some effort to deprive oneself of the powerful and luxurious charms of convex and linear functional analysis motivated by physics.</p><p style='text-indent:20px;'>These sacrifices concern only economics and other fields of life science, since physicists deal with experimental observations of objects endowed with unit of measurement by adequate processes of measurement. They can happily live in vector spaces without any guilt. This is not the case of life scientists, who have mainly history to support and validate their observations, with, sometimes, the privilege to statistically measure the frequency of some of them.</p>