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Philosophical underpinning is important in research as this leads to the investigation as per a specific paradigm. Every subject domain has a dominant paradigm in which the research is carried out. This paper surveys various journal articles in finance, specifically in financial markets contagion and spillover effects, to find the research paradigms and finds that the dominant paradigm in finance and market contagion research is functionalism-positivist. This provides opportunities to conduct research in other paradigmatic approaches. This paper explores the possibility of using an interpretivist paradigm to the financial market contagion research.

Firstly, in the determination of this paper, it is very important to note that so far nothing has been done in this regard, as it is known that a large number of different factors have been influenced. By defining this paper we will explore and illuminate the factors but also the stagnation that directly affects learning and teaching.Also, this paper will analyze the possibilities for implementing and applying an advanced learning format that directly affects this content learnable lessons comprehension by students, in our schools.We will continue to recognize those factors that are effective and have impacted on this area of learning.Students with such problems have a variety of difficulties, focusing on attention, having difficulties in performing tasks and passing quickly from one activity to another etc.These learners also show other behaviors such as: they are often confused, forget things, do not care, do not repeat, develop excessive conversations, or move often in the classroom etc.In addition paper also has analyzed the theoretical and practical aspect of students in learning and teaching.

Several approaches to second language teaching have been proposed since the 19th century. Despite these changes in the landscape of second language teaching task-based language teaching (TBLT) remains to be prevailing approach in language classrooms. However, many English language teachers lack full awareness on what TBLT is and how it can be efficiently implemented in their respective classrooms particularly in Asian classrooms using the most current language teaching and learning principles. This paper, therefore, sought to provide insights on implementing TBLT in ESL classrooms from the sociocognitive-transformative lens. The first section of the paper provides practitioners (textbook writers, teacher, curriculum developers) extensive insights on the principles underpinning TBLT and how these principles can be put into practice in language classrooms. It also presents how various language teaching theories, principles, and approaches can be integrated in teaching grammar using TBLT. The second section briefly discusses the sociocognitive-transformative approach and how TBLT can be implemented using such an approach with the aim to address the challenges and issues confronted by teachers when using TBLT. Some implications for classroom practices and research are discussed.

The present paper studies the time-consistent solutions to an investment-reinsurance problem under a mean-variance framework. The paper is distinguished from other literature by taking into account the interests of both the insurer and reinsurer jointly. The claim process of the insurer is governed by a Brownian motion with a drift. A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle. Both the insurer and the reinsurer are assumed to invest in a risky asset, which is distinct for each other and driven by a constant elasticity of variance model. The optimal decision is formulated on a weighted sum of the insurer’s and reinsurer’s surplus processes, where the weight can be viewed as a regularization parameter to balance the importance of each party in the decision. Upon a verification theorem, which is established with a formal proof for a more general problem, explicit solutions are obtained for the proposed investment-reinsurance model. Moreover, numerous mathematical analysis and numerical examples are given to demonstrate those derived results as well as the economic meanings behind.

This paper contains two parts clearly differentiated: a survey study about the use of monotonicity constraints in screening problems, and a research work extending the space of solutions in agency theory to non-smooth or even discontinuous action profiles. Specifically, we first systematize and compare, under a wide variety of assumptions on the endogenous variables of the model, existing approaches used for the derivation of necessary conditions in screening problems containing monotonicity constraints. Then, after identifying the most robust methods to generalize previous results, the paper derives a complete characterization of optimum contracts in the model of Jullien (2000), without resort to the usual continuity and smoothness assumptions on allocation functions. In this way, we conclude that most results in Jullien (2000) continue holding if, instead of the mentioned assumptions, the endogenous variables of the problem satisfy some weak regularity condition. Moreover, when the reservation utility fails to be type-dependent, as happens for instance in Guesnerie and Laffont (1978), the characterization of optimal contracts still holds without the need of imposing the referred regularity condition.

In this paper, we study a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates as well as the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study that investigates the small sample behaviour of our procedure. Finally, we illustrate our method by applying it to a series of global temperature anomalies.

Distributed order fractional differential equations are efficient in describing physical phenomena because of the differential order distribution. In this paper, the distributed order time-fractional reaction-diffusion equation is considered in the sense of Caputo fractional derivative. A hybrid method is developed based on the Moving Kriging (MK) interpolation and finite difference method for solving this distributed order equation. First, the distributed integral is discretized by the $M$-point Gauss Legendre quadrature rule. Then, the $L2-1_{\sigma}$ method is applied to approximate the solution of the fractional derivative discretization. Also, the unconditionally stability and rate of convergence $O(\tau^{2})$ of the time-discrete technique are illustrated. Furthermore, the MK interpolation is applied in the space variables discretization. Finally, some examples are presented to indicate the efficiency of this method and endorsement the theoretical results.

With the rapid development of urbanization, the metro becomes more and more important for people’s travel in big cities. To quantitatively describe metro passenger flows on congested transfer routes, this paper introduces a dynamic model based on automated data from the automatic fare collection (AFC) and automatic vehicle location (AVL) systems. An expectation maximization (EM) algorithm is proposed to compute the maximum likelihood estimates of unknown parameters in our model. Our model can yield a systematic analysis of one-transfer passenger flows on both population and individual aspects. Important characteristics, including transfer time, boarding probabilities, walking time, passenger-to-train assignment probabilities, and total travel time, can be inferred using only the AFC and AVL data. We provide a case study on the Beijing metro. Detailed analysis results based on our model are given. We also present a cross-validation method to validate our model with real data.

Today, plans to protect historic buildings focus on managing architectural heritage sustainably. Technical teams, such as architects and restorers, use massive data acquisition techniques, so an identification mechanism is required to select geometrical similarity patters to support hypothesis that guarantee historical data. Moreover, computational methods are required to understand the role of organic shapes in historic buildings. This paper first describes an extensive review of the literature and then the algorithms and methods to compare and to detect similar geometrical elements and complex patterns in architecture and archaeology. For this purpose, two key aspects are considered: the metric standpoint and historical-graphical features of the 3D models, i.e., composition, techniques, styles, and historical-graphical documentary sources. Research implies testing several methodological lines to know the similarity degree of complex organic shapes in architectural details through statistical analysis, software to assess point clouds, and complex curve analysis. The results have shown that the three procedures can be compared and that the bases of the pillars of both the Cathedral of Seville and the churches in Carmona, Jerez, and Morón are very similar; however, the base of the pillar of the church in Carmona presents scalability variations. © 2022 by the authors.

While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory.

Face Parsing aims to partition the face into different semantic parts, which can be applied into many downstream tasks, e.g., face mask up, face swapping, and face animation. With the popularity of cameras, it is easier to acquire facial images. However, pixel-wise manually labeling is time-consuming and labor-intensive, which motivates us to explore the unlabeled data. In this paper, we present a self-supervised learning method attempting to make full use of the unlabeled facial images for face parsing. In particular, we randomly mask some patches in the central area of facial images, and the model is required to reconstruct the masked patches. This self-supervised pretraining is capable of making the model capture facial feature representations through these unlabeled data. After self-supervised pretraining, the model is fine-tuned on a few labeled data for the face parsing task. Experimental results show that the model achieves better performance for face parsing assisted by the self-supervised pretraining, which greatly decreases the labeling cost. Our approach achieves 74.41 mIoU on the LaPa test set fine-tuned on only 0.2% of the labeled data of the whole training data, surpassing the model that is directly trained by a large margin of +5.02 mIoU. In addition, our approach achieves a new state-of-the-art on the LaPa and CelebAMask-HQ test set.

Let Σ+ be the set of all finite words over a finite alphabet Σ. A word u is called a strict prefix of a word v, if u is a prefix of v and there is no other way to show that u is a subword of v. A language L⊆Σ+ is said to be prefix-strict, if for any u,v∈L, u is a subword of v always implies that u is a strict prefix of v. Denote the class of all prefix-strict languages in Σ+ by P(Σ+). This paper characterizes P(Σ+) as a universe of a model of the free object for the ai-semiring variety satisfying the additional identities x+yx≈x and x+yxz≈x. Furthermore, the analogous results for so-called suffix-strict languages and infix-strict languages are introduced.

In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the H\'enon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic or not, depending on the filter coefficients. The dynamics of the system presents complex behavior, including cascades of bifurcations, coexistence of attractors, crises, and "shrimps". The obtained results are relevant in the context of bandlimited chaos-based communication systems, that have recently been proposed in the literature., Comment: Final version published in Chaos, Solitons & Fractals (2022)

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.

Predicting and identifying suspicious activities before hand is highly beneficial because it results in increased protection in video surveillance cameras’. Detecting and predicting human's action before it is carried out has a variety of uses like autonomous robots, surveillance, and health care. The main focus of the paper is on automated recognition of human actions in surveillance videos. 3DCNN (3 Dimensional Convolutional Neural Network) is based on 3D convolutions, there by capturing the motion information encoded in multiple adjacent frames. The 3DCNN is combined with Long short team memory (LSTM) and Bidirectional LSTM for prediction of abnormal events from past observations of events in video stream. It is observed that 3DCNN with LSTM resulted in increased accuracy compared to 3DCNN with Bidirectional LSTM. The experiments were carried out on UCF crime Dataset.

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest clearing payment and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component that contains more than one agent is called a cycle, and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a strictly positive endowment. The division rule used by a cyclical agent with a strictly positive endowment should be positive monotonic, and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Because division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. As a final contribution of the paper, we exhibit the relationship between the uniqueness of clearing payment matrices and the continuity of bankruptcy rules, a property that is very much desired for stability of financial systems. Funding: This research was supported by the Higher Education Institutional Excellence Program 2020 of the Ministry of Innovation and Technology in the framework of the “Financial and Public Services” research project [Grant TKP2020-IKA-02] at Corvinus University of Budapest. P. Csóka received funding from the National Research, Development and Innovation Office [Grants K-120035 and K-138826].

Recently, the nonlinear dynamics of memristor has attracted much attention. In this paper, a novel fourdimensional hyper-chaotic system (4D-HCS) is proposed by introducing a tri-valued memristor to the famous L¨u system. Theoretical analysis shows that the 4D-HCS has complex chaotic dynamics such as hidden attritors and coexistent attractors, and it has larger maximum Lyapunov exponent and chaotic parameter space than the original L¨u system. We also experimentally analyze the dynamics behaviors of the 4D-HCS in aspects of the phase diagram, Poincar´e mapping, bifurcation diagram, Lyapunov exponential spectrum, and the correlation coefficient, and the analysis results show the complex dynamic characteristics of the proposed 4D-HCS. In addition, the comparison with binary-valued memristorbased chaotic system shows that the 4D-HCS has unique characteristics such as hyper-chaos and coexistent attractors. To show the easy implementation of the 4D-HCS, we implement the 4D-HCS in an analogue circuit-based hardware platform, and the implementation results are consistent with the theoretical analysis. Finally, using the 4D-HCS, we design a pseudorandom number generator to explore its potential application in cryptography.

While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several results in this direction. Firstly, when $k = 1$, the tightest upper bound on the probability of the union of $n$ pairwise independent events is provided in closed-form for any input marginal probability vector $\mathbf{p} \in [0,1]^n$. To prove the result, we show the existence of a positively correlated Bernoulli random vector with transformed bivariate probabilities, which is of independent interest. Building on this, we show that the ratio of the Boole union bound and the tight pairwise independent bound is upper bounded by $4/3$ and that the ratio is attained. Applications of the result in correlation gap analysis and distributionally robust bottleneck optimization are discussed. The result is extended to find the tightest lower bound on the probability of the intersection of $n$ pairwise independent events. Secondly, for any $k \geq 2$ and input marginal probability vector $\mathbf{p} \in [0,1]^n$, new upper bounds are derived by exploiting ordering of probabilities. Numerical examples are provided to illustrate when the bounds provide improvement over existing bounds. Lastly, we identify specific instances when the existing and the new bounds are tight, for example, with identical marginal probabilities., 42 pages, 6 figures

While single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower games that can be applied, e.g., to model strategic booking decisions in the European entry-exit gas market. For this nontrivial class of games, we develop a solution algorithm that is able to compute the complete set of Nash equilibria instead of just individual solutions or a bigger set of stationary points. Additionally, we prove that for this class of games, the solution set is finite and provide examples for instances without any Nash equilibria in pure strategies. We apply the algorithm to a case study in which we compute strategic booking and nomination decisions in a model of the European entry-exit gas market system. Finally, we use our algorithm to provide a publicly available test library for the considered class of multi-leader multi-follower games. This library contains problem instances with different economic and mathematical properties so that other researchers in the field can test and benchmark newly developed methods for this challenging class of problems.

In this paper, we analyze the tree reconstruction problem, which is to determine whether symbols at the nth level of the tree provide information on the root as n→∞.This problem has wide applications in various fields such as biology, information theory, and statistical physics, and its close connections to the clustering problem in the setting of the stochastic block model (SBM) have been well established. Inspired by the recently proposed q1+q2 SBM, we extend the classical works on the Ising model (Borgs et al. [2006]) and the Potts model (Sly [2011]), by studying a general model which incorporates the characteristics of both Ising and Potts through different in-community and out-community transition probabilities, and rigorously establishing the exact conditions for reconstruction.

Poisson processes are widely used to model the occurrence of similar and independent events. However they turn out to be an inadequate tool to describe a sequence of (possibly differently) interacting events. Many phenomena can be modelled instead by Hawkes processes. In this paper we aim at quantifying how much a Hawkes process departs from a Poisson one with respect to different aspects, namely, the behaviour of the stochastic intensity at jump times, the cumulative intensity and the interarrival times distribution. We show how the behaviour of Hawkes processes with respect to these three aspects may be very irregular. Therefore, we believe that developing a single measure describing them is not efficient, and that, instead, the departure from a Poisson process with respect to any different aspect should be separately quantified, by means of as many different measures. Key to defining these measures will be the stochastic intensity and the integrated intensity of a Hawkes process, whose properties are therefore analysed before introducing the measures. Such quantities can be also used to detect mistakes in parameters estimation.

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool in decision theory. As our main results, we characterize distributional transforms satisfying various properties, and this includes an equivalent set of conditions which forces a distributional transform to be a probability distortion. As the first application, we construct new risk measures using distributional transforms. Sufficient and necessary conditions are given to ensure the convexity or coherence of the generated risk measures. In the second application, we introduce a new method for sensitivity analysis of risk measures based on composition groups of probability distortions. Finally, we construct probability distortions describing a change of measures with an example in option pricing.

This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of p-values without making any assumptions about their dependence structure. An old result by R\"uschendorf and, independently, Meng implies that the p-values can be combined by scaling up their arithmetic mean by a factor of 2 (and no smaller factor is sufficient in general). A similar result about the geometric mean (Mattner) replaces 2 by $e$. Based on more recent developments in mathematical finance, specifically, robust risk aggregation techniques, we extend these results to generalized means; in particular, we show that $K$ p-values can be combined by scaling up their harmonic mean by a factor of $\ln K$ (asymptotically as $K\to\infty$). This leads to a generalized version of the Bonferroni-Holm procedure. We also explore methods using weighted averages of p-values. Finally, we discuss the efficiency of various methods of combining p-values and how to choose a suitable method in light of data and prior information., Comment: 35 pages, 3 tables, 3 figures; the main changes: correcting minor mistakes and improving the presentation

In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, the complexity of solving which is related to characterizing a suitable projection of the convex hull of the set $$\{(\mathbf x , \mathbf x {} \mathbf x '): \mathbf x \in \mathcal {X}\}$$ where $$\mathcal {X}$$ is the feasible region. In some cases, this lends itself to efficient representations that result in polynomial-time solvable instances, most notably for the distributionally robust appointment scheduling problem with random job durations as well as for computing tight bounds in the newsvendor problem, project evaluation and review technique networks and linear assignment problems. To the best of our knowledge, this is the first example of a distributionally robust optimization formulation for appointment scheduling that permits a tight polynomial-time solvable semidefinite programming reformulation which explicitly captures partially known correlation information between uncertain processing times of the jobs to be scheduled. We also discuss extensions where the random coefficients are assumed to be non-negative and additional overlapping correlation information is available.

This paper finds optimal portfolios for the reference-dependent preferences by Kőszegi and Rabin with piecewise linear gain–loss utility in a one-period model with a safe and a risky asset. If the return of the risky asset is highly dispersed relative to its potential gains, two personal equilibria arise, one of them including risky investments and the other one only safe holdings. In the same circumstances, the risky personal equilibrium entails market participation that decreases with loss aversion and gain–loss sensitivity, whereas the preferred personal equilibrium is sensitive to market and preference parameters. Relevant market parameters are not the expected return and standard deviation, but rather the ratio of expected gains to losses and the Gini index of the return.

In this paper we derive exact closed-form density functions of the generalized Verhulst process (see Mackevicius (2015), Jakubowski and Wisniewolski (2015)), and the Bessel process with a constant drift (see Coman et al (1998), Linetsky (2004)), which have applications in mathematical biology and queueing theory. We propose a generic probabilistic method for deriving exact closed-form density functions for these two diusion processes based on a novel application of the exponential measure change in Palmowski and Rolski (2002) and Hurd and Kuznetsov (2008), together with formulae in Borodin and Salminen (2015). Our study generalizes several known results in the literature: Proposition 2.1 generalizes results of Theorem 2 and Theorem 3 in Jakubowski and Wisniewolski (2015) to the case of the generalized Verhulst process. Proposition 2.3 provides the exact closed-form density for a Bessel process with a constant drift, and it provides an alternative expression to the spectral expansion given in Proposition 1 of Linetsky (2004).

This paper deals with the problem of quantifying the impact of model misspecification when computing general expected values of interest. The methodology that we propose is applicable in great generality; in particular, we provide examples involving path-dependent expectations of stochastic processes. Our approach consists of computing bounds for the expectation of interest regardless of the probability measure used, as long as the measure lies within a prescribed tolerance measured in terms of a flexible class of distances from a suitable baseline model. These distances, based on optimal transportation between probability measures, include Wasserstein’s distances as particular cases. The proposed methodology is well suited for risk analysis and distributionally robust optimization, as we demonstrate with applications. We also discuss how to estimate the tolerance region nonparametrically using Skorokhod-type embeddings in some of these applications.

In this paper, in a time-homogeneous diffusion setting, we study a sequence of last passage times of generalized drawdown processes before the first passage time of another monitoring generalized drawdown process. These quantities are closely related to consecutive small market downward movements before a final big market crash modeled by the first passage time of the monitoring generalized drawdown process. Our theoretical framework simultaneously incorporates the first passage time, the absolute and relative drawdown times, and generalizes the scope of (Zhang and Hadjiliadis Methodol Comput Appl Probab 14(8):739–752 2012). We explicitly determine the path decompositions bridging these random times, the stochastic differential equations (SDE) governing each of the path fragments, and derive the Laplace transform of durations between any two of these random times. Applications include designing various risk measures summarizing several market information (e.g. historical maximum/minimum, absolute drawdown, relative drawdown) altogether. They allow us to study, in a microscopic way, a sequence of smaller drawdowns (signals) before a big drawdown (market crash) actually realizes. They can have applications to the detection of a potential market crash from signals of market drawdowns. We illustrate our results using a drifted Brownian motion.

The notion of “tail risk” has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures that quantify the tail risk, that is, the behaviour of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, value at risk (VaR) and expected shortfall, are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.

Many optimization problems in probabilistic combinatorics and mass transportation impose fixed marginal constraints. A natural and open question in this field is to determine all possible distributions of the sum of random variables with given marginal distributions; the notion of joint mixability is introduced to address this question. A tuple of univariate distributions is said to be jointly mixable if there exist random variables, with respective distributions, such that their sum is a constant. We obtain necessary and sufficient conditions for the joint mixability of some classes of distributions, including uniform distributions, distributions with monotone densities, distributions with unimodal-symmetric densities, and elliptical distributions with the same characteristic generator. Joint mixability is directly connected to many open questions on the optimization of convex functions and probabilistic inequalities with marginal constraints. The results obtained in this paper can be applied to find extreme scenarios on risk aggregation under model uncertainty at the level of dependence.

This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More generally, we also derive an error estimate for an asymptotic expansion around a general partially elliptic diffusion and a more general Wiener functional, which is applicable to various important valuation and risk management tasks in the financial business such as the ones for multidimensional diffusion and nondiffusion models. In particular, we take the Malliavin calculus approach, and estimate the error bounds for the Malliavin weights of both the coefficient and the residual terms in the expansions by effectively applying the properties of Kusuoka-Stroock functions introduced by Kusuoka [Kusuoka S (2003) Malliavin calculus revisited. J. Math. Sci. Univ. Tokyo 10:261–277.] functions. Moreover, a numerical experiment under the Heston-type model confirms the effectiveness of our method.

This paper, using a six-region dynamic stochastic general equilibrium model of the world economy, assesses the output and current account implications of permanent oil supply shocks hitting the world economy. For modest-sized shocks and conventional production technologies, the effects are modest. But for larger shocks, for elasticities of substitution that decline as oil usage is reduced to a minimum, and for production functions in which oil acts as a critical enabler of technologies, output growth could drop significantly. Also, oil prices could become so high that smooth adjustment, as assumed in the model, may become very difficult.

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters.

Ubiquitous computing means network connectivity everywhere, linking devices and systems as small as a drawing pin and as large as a worldwide product distribution chain. What could happen whenpeopleare so readily networked? This paper explores issues arising from two possible emerging models of ubiquitous human computing: fungible networked brainpower and collective personal vital sign monitoring.

An explicit description of the convex hull of solutions to the uncapacitated lot sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough to describe the convex hull of solutions. We give polynomial separation algorithms for some special cases. Finally, we report a summary of computational experiments with our inequalities that illustrates their effectiveness.

In this paper a portfolio problem is considered where trading in the risky asset is stopped if a state process hits a predefined barrier. This state process need not to be perfectly correlated with the risky asset. We give a representation result for the value function and provide a verification theorem. As an application, we explicitly solve the problem by assuming that the state process is an arithmetic Brownian motion. Then the result is used as a starting point to solve and analyze a portfolio problem with default risk modeled by the Black-Cox approach. Finally, we discuss how our results can be applied to a portfolio problem with stochastic interest rates and default risk modeled by the approach of Briys and de Varenne.

In this paper we extend the smoothing technique (Nesterov in Math Program 103(1): 127–152, 2005; Nesterov in Unconstrained convex mimimization in relative scale, 2003) onto the problems of semidefinite optimization. For that, we develop a simple framework for estimating a Lipschitz constant for the gradient of some symmetric functions of eigenvalues of symmetric matrices. Using this technique, we can justify the Lipschitz constants for some natural approximations of maximal eigenvalue and the spectral radius of symmetric matrices. We analyze the efficiency of the special gradient-type schemes on the problems of minimizing the maximal eigenvalue or the spectral radius of the matrix, which depends linearly on the design variables. We show that in the first case the number of iterations of the method is bounded by $$O({1}/{\epsilon})$$, where $$\epsilon$$ is the required absolute accuracy of the problem. In the second case, the number of iterations is bounded by $${({4}/{\delta})} \sqrt{(1 + \delta) r\, \ln r }$$, where δ is the required relative accuracy and r is the maximal rank of corresponding linear matrix inequality. Thus, the latter method is a fully polynomial approximation scheme.

This paper proposes a new nonparametric estimator for general regression functions with multiple regressors. The method used here is motivated by a remarkable result derived by Kolmogorov (1957) and later tightened by Lorentz (1966). In short, any continuous function f(x_1,...,x_d) has the representation G[a_1 P_1(x_1) + ... + a_d P_1(x_d)] + ... + G[a_1 P_m(x_1) + ... + a_d P_m(x_d)], m = 2d+1, where G(.) is a continuous function, P_k(.), k=1,...,2d+1, is Lipschitz of order one and strictly increasing, and a_j, j=1,...,d, is some constant. Generalizing this result, we propose the following estimator, g_1[a_1,1 p_1(x_1) + ... + a_d,1 p_1(x_d)] + ... + g_m[a_1,d P_m(x_1) + ... + a_d,d p_m(x_d)], where both g_k(.) and p_k(.) are twice continuously differentiable. These functions are estimated using regression cubic B-splines, which have excellent numerical properties. This problem has been previously intractable because there existed no method for imposing monotonicity on the p_k(.)'s, a priori, such that the estimator is dense in the set of all monotonic cubic B-splines. We derive a method that only requires 2(r+1)+1 restrictions, where r is the number of interior knots. Rates of convergence in L_2 are the same as the optimal rate for the one-dimensional case. A simulation experiment shows that the estimator works well when optimization is performed by using the back-fitting algorithm. The monotonic restriction has many other applications besides the one presented here, such as estimating a demand function. With only r+2 more constraints, it is also possible to impose concavity.

This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games.