Relative Convexity Research Articles

CFO pay convexity, risk taking and corporate hedging

AbstractWe study how a CFO's risk‐taking incentives affect corporate hedging by utilising hand‐collected data from 2009 to 2019 on corporate hedging and managerial compensation for a sample of US oil and gas firms. The relative convexity of CFO equity compensation negatively affects the likelihood and extent of hedging. When the CFO and CEO have diverging risk‐taking incentives, the relative convexity of the CFO's equity payoff prevails over that of the CEO. This evidence underscores the primary role of the CFO in steering a firm's hedging strategy.

Total positivity and relative convexity of option prices

This paper studies total positivity and relative convexity properties in option pricing models. We introduce these properties in the Black-Scholes setting by showing the following: out-of-the-money calls are totally positive in strike and volatility; out-of-the-money puts have a reverse sign rule property; calls and puts are convex with respect to at-the-money prices; and relative convexity of option prices implies a convexity-in-time property of the underlying. We then extend these properties to other models, including scalar diffusions, mixture models, and certain Lévy processes. We show that relative convexity typically holds in time-homogeneous local volatility models through the Dupire equation. We develop implications of these ideas for empirical option prices, including constraints on the at-the-money skew. We illustrate connections with models studied by Peter Carr, including the variance-gamma, CGMY, Dagum, and logistic density models.

Paranasal Augmentation: A Viable and Simplified Modality With Diced Expanded Polytetrafluoroethylene.

A flat or concave lower midface profile is generally considered less attractive. Paranasal augmentation is usually performed to move paranasal deficiency to relative convexity. Herein, we present a viable and simplified modality with diced expanded polytetrafluoroethylene to correct paranasal deficiency. Between February of 2020 and April of 2021, 19 patients underwent procedures to correct paranasal deficiency. Paranasal augmentation was performed with diced expanded polytetrafluoroethylene. All procedures were performed via intranasal approach. Preoperative and postoperative photographs were taken. Of these 19 patients (18 women and 1 man), deficiency of 18 patients were caused by congenital factors and 1 by cleft deformities. All but 1 procedures were carried out bilaterally. Procedures were performed in conjunction with additional operations mainly including rhinoplasty and minimally invasive midface lift. Age of patients ranged from 19 to 57 years, with a mean of 37 years. Follow-up time ranged from 8 to 22 months, with a mean of 12.6 months. All patients were satisfied with esthetic improvement and facial holistic profile. No severe complications and reoperation arisen in any of the patients. Temporary discomfort involved foreign body sensation in 1 case and numbness in 2 cases. The present technique provides a viable and simplified method to give the face a more balanced appearance and achieves esthetically superior results.

Total Positivity and Relative Convexity of Option Prices

Total Positivity and Relative Convexity of Option Prices

Second-order stochastic comparisons of order statistics

We study the problem of comparing ageing patterns of lifetimes of k-out-of-n systems with i.i.d. components. Mathematically, this reduces to being able to decide about a stochastic ordering relationship between different order statistics. We discuss such relationships with respect to second-order stochastic dominance, obtaining characterizations through the verification of relative convexity with respect to a suitably chosen reference distribution function. We introduce a hierarchy of such reference functions leading to classes, each expressing different and increasing knowledge precision about the distribution of the components lifetimes. Such classes are wide enough to include popular families of distributions, such as, for example, the increasing failure rate distributions. We derive sufficient dominance conditions depending on the identification of the class which includes the component lifetimes. We discuss the applicability of this method and characterize a test for the relative convexity, as this notion plays a central role in the proposed approach.

Modular verification of heap reachability properties in separation logic

The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First, any heap modification may affect an unbounded number of reference chains, which complicates modular verification, in particular, framing. Second, general graph reachability is not supported by first-order SMT solvers, which impedes automatic verification. In this paper, we present a modular specification and verification technique for reachability properties in separation logic. For each method, we specify reachability only locally within the fragment of the heap on which the method operates. We identify relative convexity, a novel relation between the heap fragments of a client and a callee, which enables (first-order) reachability framing, that is, extending reachability properties from the heap fragment of a callee to the larger fragment of its client, enabling precise procedure-modular reasoning. Our technique supports practically important heap structures, namely acyclic graphs with a bounded outdegree as well as (potentially cyclic) graphs with at most one path (modulo cycles) between each pair of nodes. The integration into separation logic allows us to reason about reachability and other properties in a uniform way, to verify concurrent programs, and to automate our technique via existing separation logic verifiers. We demonstrate that our verification technique is amenable to SMT-based verification by encoding a number of benchmark examples into the Viper verification infrastructure.

Certain unified integral inequalities in connection with quantum fractional calculus

Some unified integral inequalities involving quantum fractional calculus are obtained via the functions having classical and relative convexity property

ITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS

Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.

Hardy-Littlewood-Polya theorem of majorization in the framework of generalized convexity

Based on a new concept of generalized relative convexity, a large extension of Hardy-Littlewood-Polya theorem ´ of majorization is obtained. Several applications escaping the classical framework of convexity are included.

From Isovist to Spatial Perception: Wayfinding in Historic Quarter

Based on the assumption that human behaviours are mainly affected by physical and animate environments, this empirical research takes the changeful and complex historical district in Tainan to observe wayfinding behaviours. An a priori analysis of the isovist fields is conducted to identify spatial characteristics. Three measures, the relative area, convexity, and circularity, are applied to scrutinize the possible stopping points, change of speed, and route choices. Accordingly, an experiment is carried out to observe spatial behaviours and different influences of social stimuli. Results show that social interactions afford groups and pairs to perform better than individual observers in wayfinding.© 2016. The Authors. Published for AMER ABRA by e-International Publishing House, Ltd., UK. Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies, Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, MalaysiaKeywords: wayfinding; isovist; spatial perception and social stimuli; historic quarter

Supplier Evasion of a Buyer’s Audit: Implications for Motivating Supplier Social and Environmental Responsibility

Prominent buyers’ brands have been damaged because their suppliers caused major harm to workers or the environment, e.g., through a deadly factory fire or release of toxic chemicals. How can buyers motivate suppliers to exert greater care to prevent such harm? This paper characterizes a “backfiring condition” under which actions taken by prominent buyers (increasing auditing, publicizing negative audit reports, providing loans to suppliers) motivate a supplier to exert greater effort to pass the buyer’s audit by hiding information and less care to prevent harm. Intuitively appealing actions for a buyer (penalizing a supplier for harming workers or the environment, or for trying to deceive an auditor) may be similarly counterproductive. Contrary to conventional wisdom, squeezing a supplier’s margin (by reducing the price paid to the supplier or increasing wages for workers) motivates the supplier to exert greater care to prevent harm—under the backfiring condition. Whereas the necessary and sufficient condition depends on the relative convexity of the supplier’s hiding cost function, a simple sufficient condition is that the supplier is likely to successfully hide information from the auditor, in equilibrium. Anecdotal evidence suggests that the backfiring condition is prevalent or becoming increasingly so. Similar insights apply to mitigation of unauthorized subcontracting.

Variational Bayesian Matrix Factorization for Bounded Support Data.

A novel Bayesian matrix factorization method for bounded support data is presented. Each entry in the observation matrix is assumed to be beta distributed. As the beta distribution has two parameters, two parameter matrices can be obtained, which matrices contain only nonnegative values. In order to provide low-rank matrix factorization, the nonnegative matrix factorization (NMF) technique is applied. Furthermore, each entry in the factorized matrices, i.e., the basis and excitation matrices, is assigned with gamma prior. Therefore, we name this method as beta-gamma NMF (BG-NMF). Due to the integral expression of the gamma function, estimation of the posterior distribution in the BG-NMF model can not be presented by an analytically tractable solution. With the variational inference framework and the relative convexity property of the log-inverse-beta function, we propose a new lower-bound to approximate the objective function. With this new lower-bound, we derive an analytically tractable solution to approximately calculate the posterior distributions. Each of the approximated posterior distributions is also gamma distributed, which retains the conjugacy of the Bayesian estimation. In addition, a sparse BG-NMF can be obtained by including a sparseness constraint to the gamma prior. Evaluations with synthetic data and real life data demonstrate the good performance of the proposed method.

Environmental Statistics and Optimal Regulation

Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies - such as constitutive expression or graded response - for regulating protein levels in response to environmental inputs. We propose a general framework - here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient - to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones.

Relative convexity and its applications

We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the Hardy–Littlewood–Pólya theorem of majorization is proved and a new insight is given into the problem of risk aversion in mathematical finance.

Environmental statistics and optimal regulation.

Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies–such as constitutive expression or graded response–for regulating protein levels in response to environmental inputs. We propose a general framework–here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient–to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones.

The Optimization of Finishing Train Based on Improved Genetic Algorithm

The central issue of finishing train is that we should distribute the thickness of each exit with reason and determine the rolling force and relative convexity. The optimization methods currently used are empirical distribution method and the load curve method, but they both have drawbacks. To solve those problems we established a mathematical model of the finishing train and introduced an improved Genetic Algorithm. In this algorithm we used real number encoding, selection operator of a roulette and elitist selection and then improved crossover and mutation operators. The results show that the model and algorithm is feasible and could ensure the optimal effect and convergence speed. The products meet the production requirements. DOI : http://dx.doi.org/10.11591/telkomnika.v12i5.3892

On some relative convexities

We study two types of relative convexities of convex functions f and g. We say that f is convex relative to g in the sense of Palmer (2002, 2003), if f=h(g), where h is strictly increasing and convex, and denote it by f≻(1)g. Similarly, if f is convex relative to g in the sense studied in Rajba (2011), that is if the function f−g is convex then we denote it by f≻(2)g. The relative convexity relation ≻(2) of a function f with respect to the function g(x)=cx2 means the strong convexity of f. We analyze the relationships between these two types of relative convexities. We characterize them in terms of right derivatives of functions f and g, as well as in terms of distributional derivatives, without any additional assumptions of twice differentiability. We also obtain some probabilistic characterizations. We give a generalization of strong convexity of functions and obtain some Jensen-type inequalities.

The Optimal Allocation of Finishing Train in Steel Rolling Based on Improved Genetic Algorithm

The central issue of finishing train is that we should distribute the thickness of each exit with reason and determine the rolling force and relative convexity. The optimization methods currently used are empirical distribution method and the load curve method, but they both have drawbacks. To solve those problems we established a mathematical model of the finishing train and introduced an improved Genetic Algorithm. In this algorithm we used real number encoding, selection operator of a roulette and elitist selection and then improved crossover and mutation operators. The results show that the model and algorithm is feasible and could ensure the optimal effect and convergence speed. The products meet the production requirements.

An Association of Lateral Knee Sagittal Anatomic Factors with Non-Contact ACL Injury: Sex or Geometry?

Lateral tibiofemoral articular geometry may play a role in the development of non-contact anterior cruciate ligament (ACL) injuries. We hypothesized that athletes who had sustained an ACL injury would demonstrate more highly convex articular surfaces in the lateral compartment of the knee compared with activity-matched athletes who had not sustained an ACL injury, and that women would demonstrate greater absolute and relative convexity of these articular surfaces than men. One hundred and twelve athletes with a non-contact ACL injury and sixty-one activity-matched athletes without an ACL injury were studied. Three blinded observers measured the articular geometry in the mid-lateral sagittal plane with use of magnetic resonance imaging. The tibial plateau radius of curvature (TPr), distal femoral radius of curvature (Fr), maximal femoral anteroposterior articular length (FAP), and maximal tibial anteroposterior articular length (TPAP) were recorded. The Fr:TPr and FAP:TPAP ratios were also calculated to adjust for size variations. The intraclass correlation coefficient and the two-sample Student t test were used to compare quantitative variables. All data were found to follow a normal distribution. When data for male and female patients were combined, the mean TPr, Fr, and TPAP values were significantly smaller in the ACL-injured patients than in the uninjured patients (33.9 compared with 37.5 mm, p = 0.005; 24.3 compared with 25.1 mm, p = 0.04; and 31.5 compared with 33.1 mm, p = 0.007; respectively). The mean FAP value did not differ significantly between the ACL-injured and uninjured patients but the difference in the mean FAP:TPAP value was significant (p = 0.003). When only male patients were analyzed, the mean TPr, Fr, and TPAP values were also significantly smaller in the ACL-injured patients than in the uninjured patients (35.5 compared with 41.1 mm, p = 0.002; 25.5 compared with 26.7 mm, p = 0.001; and 33.0 compared with 35.5 mm, p = 0.0002; respectively). The mean FAP value did not differ significantly between the ACL-injured and uninjured male patients, but the difference in the mean FAP:TPAP value was significant (p = 0.0005). In contrast, when only female patients were analyzed, none of the mean values differed significantly between the ACL-injured and uninjured patients. The FAP:TPAP and Fr:TPr values did not differ significantly among the ACL-injured male patients, injured female patients, and uninjured female patients. All female patients (both ACL-injured and uninjured) and ACL-injured male patients shared a common lateral knee geometry characterized by a smaller tibial plateau length relative to the femur and by more convex articulating surfaces of the proximal aspect of the tibia and the distal aspect of the femur. Shorter, more highly convex articulating surfaces may be inherently less stable with regard to anterior tibial translation and rotation. These findings may partially explain the greater overall predisposition of women compared with men toward ACL injury as well as why some studies have demonstrated no sex differences in graft reinjury after ACL reconstruction.

Relative convexity and quadrature rules for the Riemann-Stieltjes integral

We develop Trapezoid, Midpoint, and Simpson's rules for the Riemann-Stieltjes in- tegral, the latter two being new. These rules are completely natural when the notion of relative convexity is used.