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It is common in international football for the same agent to be paid both commission fees by the purchasing club for negotiating a player salary and a transfer fee. This dual representation creates a potential conflict of interest for the agent. The agent may not negotiate the highest salary for the player if a higher salary reduces the likelihood of a successful transfer by lowering the resources available for the transfer fee. We construct a gamble model of the transfer process and simulate the ex-ante agent commissions rates, expected player salary, transfer fee and club profit under the assumption of dual representation where the buying club pays all agent commissions. The assumption that the quality of the agent increases with the commission rate is essential to the model. Both the player and the club are better off when the club pays both commissions, however the agent is worse off. [ABSTRACT FROM AUTHOR]

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation A X B + C Y D ≈ E , where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH -representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation A X B + C Y D ≈ E . The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a structural decomposition for strong comonotonic additive systemic risk measures. Third, when both the single-firm risk measure and the aggregation function in the structural decomposition are convex, we also provide a dual representation for it. Last, examples are given to illustrate the proposed systemic risk measures. Comparisons with existing systemic risk measures are also provided. [ABSTRACT FROM AUTHOR]

We develop a regression-based primal-dual martingale approach for solving discrete time, finite-horizon MDPs. The state and action spaces may be finite or infinite (but regular enough) subsets of Euclidean space. Consequently, our method allows for the construction of tight upper and lower-biased approximations of the value functions, providing precise estimates of the optimal policy. Importantly, we prove error bounds for the estimated duality gap featuring polynomial dependence on the time horizon. Additionally, we observe sublinear dependence of the stochastic part of the error on the cardinality/dimension of the state and action spaces. From a computational perspective, our proposed method is efficient. Unlike typical duality-based methods for optimal control problems in the literature, the Monte Carlo procedures involved here do not require nested simulations. [ABSTRACT FROM AUTHOR]

Barr and Kirkorian (2023) summarize decades of research about young children's learning and transfer from screen media, offer a new theoretical model of factors involved in early multimedia learning, and suggest a future research agenda to study learning from commercial media products "in the wild" of everyday family life outside the lab. In this commentary, the authors offer background on the development of symbolic understanding and "pictorial competence" for young children's learning from screen media and attempt to deepen the discussion of cognitive factors and individual differences that affect early learning. [ABSTRACT FROM AUTHOR]

We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic properties of quantile functions and can thus be easily implemented in any graduate course on risk measures. As a byproduct, we obtain a new proof of the subadditivity of Expected Shortfall. [ABSTRACT FROM AUTHOR]

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation AXB+CYD≈E, where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH-representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation AXB+CYD≈E. The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method.

In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a structural decomposition for strong comonotonic additive systemic risk measures. Third, when both the single-firm risk measure and the aggregation function in the structural decomposition are convex, we also provide a dual representation for it. Last, examples are given to illustrate the proposed systemic risk measures. Comparisons with existing systemic risk measures are also provided.

Risk forms are real functionals of two arguments: a bounded measurable function on a Polish space and a probability measure on that space. They are convenient mathematical structures adapting the coherent risk measures to the situation of a variable reference probability measure. We introduce a new class of risk forms called mini-batch forms. We construct them by using a random empirical probability measure as the second argument and by post-composition with the expected value operator. We prove that coherent and law invariant risk forms generate mini-batch risk forms which are well defined on the space of integrable random variables, and we derive their dual representation. We demonstrate how unbiased stochastic subgradients of such risk forms can be constructed. Then, we consider pre-compositions of mini-batch risk forms with nonsmooth and nonconvex functions, which are differentiable in a generalized way, and we derive generalized subgradients and unbiased stochastic subgradients of such compositions. Finally, we study the dependence of risk forms and mini-batch risk forms on perturbation of the probability measure and establish quantitative stability in terms of optimal transport metrics. We obtain finite-sample expected error estimates for mini-batch risk forms involving functions on a finite-dimensional space. [ABSTRACT FROM AUTHOR]

In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 2002) to the case of optimal stopping under model uncertainty, we develop a novel regression-based Monte Carlo algorithm for the approximation of the corresponding value function. The algorithm involves optimising a penalised empirical dual objective functional over a class of martingales. This formulation allows us to construct upper bounds for the optimal value with reduced complexity. Finally, we carry out a convergence analysis of the proposed algorithm and illustrate its performance by several numerical examples. [ABSTRACT FROM AUTHOR]

This study examines the impact of manipulation on the performance of 3.5‐ and 4‐year‐old children in the Give‐N task with concrete representations (sets of bottle caps and pictures of dots) and spoken number words. In this task, children were asked to give a certain number of items (cookies) using the three representational formats. Children were assigned to one of two conditions: manipulation (children could physically interact with the objects and pictures) or observation (children watched as the experimenter presented the representations). Results show that manipulation had different effects according to the age of the children. For 3.5‐year‐olds, manipulation with objects but not with pictures consisted in task‐irrelevant actions, and hindered performance. For 4‐year‐olds, however, manipulation with both concrete representations were task related and did not disrupt performance. The mere contemplation of the objects and pictures, without physically interacting with them, facilitated performance in both age groups, in comparison with number words. Emerging cardinal comprehension seems to be influenced not only by the kind of representations used by children, but also by the type of physical exploration afforded during the task. [ABSTRACT FROM AUTHOR]

The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on L 0 is fixed to characterize the family of acceptable wealths that play the role of nonnegative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices (called risk-hedging prices) of a European option. Moreover, we show that the set of all risk-hedging prices is closed under NA. At last, we provide a dual representation of the risk-measure on L 0 under some conditions. [ABSTRACT FROM AUTHOR]

Organisms and other living things grow as fractals, helping to maximize space-filling ability and transmit flow efficiently. In recent years, many studies on fractals have been carried out, mostly at a geometric level, although little work has been done on fractal properties at a structural level. In fact, the capacity of geographical objects, especially road networks, is dependent not only on the geometric distribution described by a geometric fractal dimension but also on the level of structural complexity as described by a structural fractal dimension. Past studies on a structural fractal dimension are limited to a single scale and a single representation. Because different representations could lead to different results in fractal analysis, this study aims to examine the structural fractality of urban road networks by different representations. The road networks of the 100 most populous cities in the United States were examined by three commonly used topological representations. The following results were established: Despite differences in representation, structural fractality always exists; structural fractal dimensions in stroke-based representation are obviously larger than those in segment-based representation; and scale has no obvious effects on structural fractality. These results could deepen our understanding of how urban road networks evolve. [ABSTRACT FROM AUTHOR]

The properties of risk measures in the form of infimal convolution are analyzed. The dual representation of such measures, their subdifferential, extremum conditions, representation for optimization and use in constraints are described. The results of the study are demonstrated by examples of known risk measures of such structure. This allows systematization of the available results and facilitates a potential search for new variants of risk measures. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Distortion (Denneberg in ASTIN Bull 20(2):181–190, 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia. [ABSTRACT FROM AUTHOR]

Background and aims: Children with autism spectrum condition often have specific difficulties understanding that pictorial symbols refer to real-world objects in the environment. We investigated the influence of labelling on the symbolic understanding and dual representation of children with autism spectrum condition. Methods: Children with autism spectrum condition and typically developing children were shown four coloured photographs of objects that had different functions across four separate trials. The participants were given either a novel label alongside a description of the object's function or a description of the object's function without a label. Children were then given 30 seconds to interact with an array of stimuli (pictures and objects) in a mapping test and in a generalisation test for each trial. This exploration phase allowed for spontaneous word–picture–referent mapping through free-play, providing an implicit measure of symbolic understanding. Results: We found no significant difference in word–picture–referent mapping between groups and conditions. Both groups more often performed the described action on the target object in the exploration phase regardless of condition. Conclusions and implications: Our results suggest that a spontaneous measure of symbolic understanding (such as free-play) may reveal competencies in word–picture–referent mapping in autism spectrum condition. [ABSTRACT FROM AUTHOR]

Let Ω be a Polish space with Borel σ -field F and countably generated sub σ -field G ⊂ F. Denote by L (F) the set of all bounded F -upper semianalytic functions from Ω to the reals and by L (G) the subset of G -upper semianalytic functions. Let E (⋅ | G) : L (F) → L (G) be a sublinear increasing functional which leaves L (G) invariant. It is shown that there exists a G -analytic set-valued mapping P G from Ω to the set of probabilities which are concentrated on atoms of G with compact convex values such that E (X | G) (ω) = sup P ∈ P G (ω) E P [ X ] if and only if E (⋅ | G) is pointwise continuous from below and continuous from above on the continuous functions. Further, given another sublinear increasing functional E (⋅) : L (F) → R which leaves the constants invariant, the tower property E (⋅) = E (E (⋅ | G)) is characterized via a pasting property of the representing sets of probabilities, and the importance of analytic functions is explained. Finally, it is characterized when a nonlinear version of Fubini's theorem holds true and when the product of a set of probabilities and a set of kernels is compact. [ABSTRACT FROM AUTHOR]

The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can represent bailout costs. More recently, a framework has been introduced, where institutions are supplied with capital allocations before aggregation. This yields an interpretation that is particularly useful for regulatory purposes. In each framework, the set of all feasible capital allocations leads to a multivariate risk measure. In this paper, we present dual representations for scalar systemic risk measures as well as for the corresponding multivariate risk measures concerning capital allocations. Our results cover both frameworks: aggregating after allocating and allocating after aggregation. As examples, we consider the aggregation mechanisms of the Eisenberg–Noe model as well as those of the resource allocation and network flow models. [ABSTRACT FROM AUTHOR]

A theory for set-valued functions is developed, which are translative with respect to a linear operator. It is shown that such functions cover a wide range of applications, from projections in Hilbert spaces, set-valued quantiles for vector-valued random variables, to scalar or set-valued risk measures in finance with defaultable or nondefaultable securities. Primal, dual, and scalar representation results are given, among them an infimal convolution representation, which is not so well known even in the scalar case. Along the way, new concepts of set-valued lower/upper expectations are introduced and dual representation results are formulated using such expectations. An extension to random sets is discussed at the end. The principal methodology consisted of applying the complete lattice framework of set optimization.

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

Data-driven soft sensors are crucial for predicting key quality variables in the process industry. In most processes, the dynamic characteristics are obvious, and the relationship between the primary and secondary variables is strongly nonlinear. Moreover, the worst thing is that labeled samples are usually scarce due to certain technical difficulties or measurement costs. To deal with these issues, this paper first proposes a semi-supervised manifold regularization model based on dual representation (SsMRM-DR). Then, a semi-supervised local manifold regularization model based on dual representation (SsLMRM-DR) is further proposed from the viewpoint of local manifold regularization. In the SsLMRM-DR, a space–time weighted similarity calculation method is designed to reduce the influence of measurement noise on similarity calculation. At the same time, a local manifold regularization method is developed to use unlabeled samples more efficiently and to improve the prediction accuracy and computational efficiency of the SsLMRM-DR. A numerical example and a real industrial process are used to evaluate the performance of the proposed schemes. The results show that SsLMRM-DR is effective and it has a good application prospect of soft sensors in the industry. • Temporal regularization methods cannot utilize unlabeled samples efficiently. • Space–time weighted similarity is for space correlations/time series of varaibles. • Local manifold regularization uses unlabeled samples for computational efficiency. • Strong nonlinear and dynamic problems and sample scarcity are solved concurrently. • A semi-supervised local manifold regularization model is proposed. [ABSTRACT FROM AUTHOR]

• To guarantee high fire detection rate, a L0 norm constraint is introduced into the model. • To speed training and reduce error warning rate, L1 norm PreVM and its nonlinear version is also provided. • Theoretically, we prove the existence of dual representation for the general Lp (p>=1) norm regularization problems and the kernelization of L1 norm problem with implicit feature map. • Compared to the state-of-the-art, our proposed PreVMs are superior in fire detection rate, error warning rate, and real-time fire detection. Machine learning-based fire detection/recognition is very popular in forest-monitoring systems. However, without considering the prior knowledge, e.g., equal attention on both classes of the fire and non-fire samples, fire miss-detected phenomena frequently appeared in the current methods. In this work, considering model's interpretability and the limited data for model-training, we propose a novel pixel-precision method, termed as PreVM (Preferred Vector Machine). To guarantee high fire detection rate under precise control, a new L 0 norm constraint is introduced to the fire class. Computationally, instead of the traditional L 1 re-weighted techniques in L 0 norm approximation, this L 0 constraint can be converted into linear inequality and incorporated into the process of parameter selection. To further speed up model-training and reduce error warning rate, we also present a kernel-based L 1 norm PreVM (L 1 -PreVM). Theoretically, we firstly prove the existence of dual representation for the general L p (p ≥ 1) norm regularization problems in RKHS (Reproducing Kernel Hilbert Space). Then, we provide a mathematical evidence for L 1 norm kernelization to conquer the case when feature samples do not appear in pairs. The work also includes an extensive experimentation on the real forest fire images and videos. Compared with the-state-of-art methods, the results show that our PreVM is capable of simultaneously achieving higher fire detection rates and lower error warning rates, and L 1 -PreVM is also superior in real-time detection. [ABSTRACT FROM AUTHOR]

This paper presents a study on the set of the digitizations generated by all the translations of a planar body on a square grid. First the translation vector set is reduced to a bounded subset, then the dual introduced in [1] linking the translation vector to the corresponding digitization is proved to be piecewise constant. Finally, a new algorithm is proposed to compute the digitization set using the dual. [ABSTRACT FROM AUTHOR]

This paper addresses the Entropic Value-at-Risk ( $${{\mathrm{\mathsf {EV@R}}}}$$ ), a recently introduced coherent risk measure. It is demonstrated that the norms defined by $${{\mathrm{\mathsf {EV@R}}}}$$ induce the same Banach spaces, irrespective of the confidence level. Three vector spaces, called the primal, dual, and bidual entropic spaces, corresponding with $${{\mathrm{\mathsf {EV@R}}}}$$ are fully studied. It is shown that these spaces equipped with the norms induced by $${{\mathrm{\mathsf {EV@R}}}}$$ are Banach spaces. The entropic spaces are then related to the $$L^p$$ spaces, as well as specific Orlicz hearts and Orlicz spaces. This analysis indicates that the primal and bidual entropic spaces can be used as very flexible model spaces, larger than $$L^\infty $$ , over which all $$L^p$$ -based risk measures are well-defined. The dual $${{\mathrm{\mathsf {EV@R}}}}$$ norm and corresponding Hahn-Banach functionals are presented in closed form, which are not explicitly known for the Orlicz and Luxemburg norms that are equivalent to the $${{\mathrm{\mathsf {EV@R}}}}$$ norm. The duality relationships among the entropic spaces are investigated. The duality results are also used to develop an extended Donsker-Varadhan variational formula, and to explicitly provide the dual and Kusuoka representations of $${{\mathrm{\mathsf {EV@R}}}}$$ , as well as the corresponding maximizing densities in both representations. Our results indicate that financial concepts can be successfully used to develop insightful tools for not only the theory of modern risk measurement but also other fields of stochastic analysis and modeling. [ABSTRACT FROM AUTHOR]

The choice of a risk measure reflects a subjective preference of the decision maker in many managerial or real world economic problem formulations. To assess the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We establish a one-to-one relationship between norms and risk measures, that is, we associate a norm with a risk measure and conversely, we use norms to recover a genuine risk measure. The methods allow tight comparisons of risk measures and tight lower and upper bounds for risk measures are made available whenever possible. In this way we present a general framework for comparing risk measures with applications in numerous directions. [ABSTRACT FROM AUTHOR]

We present a general framework for measuring the liquidity risk. The theoretical framework defines risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement model. The liquidity risk is defined as the risk that a security or a portfolio of securities cannot be sold or bought without causing changes in prices. The risk measures are decomposed into two terms, one measuring the risk of the future value of a given position in a security or a portfolio of securities and the other the initial cost of this position. Within the framework of coherent risk measures, the risk measures applied to the random part of the future value of a position in a determinate security are increasing monotonic and convex cash sub-additive on long positions. The contrary, in certain situations, holds for the sell positions. By using convex risk measures, we apply our framework to the situation in which large trades are broken into many small ones. Dual representation results are obtained for both positions in securities and portfolios. We give many examples of risk measures and derive for each of them the respective capital requirement. In particular, we discuss the VaR measure. [ABSTRACT FROM PUBLISHER]