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This article presents a holistic compound Poisson regression model framework to forecast number of corner kicks taken in association football. Corner kick taken events are often decisive in the match outcome and inherently arrive in batch with serial clustering pattern. Providing parameter estimates with intuitive interpretation, a class of compound Poisson regression including a Bayesian implementation of geometric-Poisson distribution are introduced. With a varying shape parameter, the corner counts serial correlation between matches is handled naturally within the Bayesian model. In this study, information elicited from cross-market betting odds was used to improve the model predictability. Margin application methods to adjust market inefficiency in raw odds are also discussed. [ABSTRACT FROM AUTHOR]

Stochastic variational inequalities (SVIs) have been used widely in modelling various optimization and equilibrium problems subject to data uncertainty. The sample average approximation (SAA) solution is an asymptotically consistent point estimator for the true solution to a stochastic variational inequality. Some central limit results and large deviation estimates for the SAA solution have been obtained. The purpose of this paper is to study the convergences in regimes of moderate deviations for the SAA solution. Using the delta method and the exponential approximation, we establish some results on moderate deviations. We apply the results to the hypotheses testing for the SVIs, and prove that the rejection region constructed by the central limit theorem has the probability of the type II error with exponential decay speed. We also give some simulations and numerical results for the tail probabilities. [ABSTRACT FROM AUTHOR]

In addition to the filter coefficients, the location of the microphone array is a crucial factor in improving the overall performance of a beamformer. The optimal microphone array placement can considerably enhance speech quality. However, the optimization problem with microphone configuration variables is non-convex and highly non-linear. Heuristic algorithms that are frequently employed take a long time and have a chance of missing the optimal microphone array placement design. We extend the Bayesian optimization method to solve the microphone array configuration design problem. The proposed Bayesian optimization method does not depend on gradient and Hessian approximations and makes use of all the information available from prior evaluations. Furthermore, Gaussian process regression and acquisition functions make up the Bayesian optimization method. The objective function is given a prior probabilistic model through Gaussian process regression, which exploits this model while integrating out uncertainty. The acquisition function is adopted to decide the next placement point based upon the incumbent optimum with the posterior distribution. Numerical experiments have demonstrated that the Bayesian optimization method could find a similar or better microphone array placement compared with the hybrid descent method and computational time is significantly reduced. Our proposed method is at least four times faster than the hybrid descent method to find the optimal microphone array configuration from the numerical results. [ABSTRACT FROM AUTHOR]

Accurate short-term load forecasting (STLF) is essential for power grid systems to ensure reliability, security and cost efficiency. Thanks to advanced smart sensor technologies, time-series data related to power load can be captured for STLF. Recent research shows that deep neural networks (DNNs) are capable of achieving accurate STLP since they are effective in predicting nonlinear and complicated time-series data. To perform STLP, existing DNNs use time-varying dynamics of either past load consumption or past power correlated features such as weather, meteorology or date. However, the existing DNN approaches do not use the time-invariant features of users, such as building spaces, ages, isolation material, number of building floors or building purposes, to enhance STLF. In fact, those time-invariant features are correlated to user load consumption. Integrating time-invariant features enhances STLF. In this paper, a fuzzy clustering-based DNN is proposed by using both time-varying and time-invariant features to perform STLF. The fuzzy clustering first groups users with similar time-invariant behaviours. DNN models are then developed using past time-varying features. Since the time-invariant features have already been learned by the fuzzy clustering, the DNN model does not need to learn the time-invariant features; therefore, a simpler DNN model can be generated. In addition, the DNN model only learns the time-varying features of users in the same cluster; a more effective learning can be performed by the DNN and more accurate predictions can be achieved. The performance of the proposed fuzzy clustering-based DNN is evaluated by performing STLF, where both time-varying features and time-invariant features are included. Experimental results show that the proposed fuzzy clustering-based DNN outperforms the commonly used long short-term memory networks and convolution neural networks. [ABSTRACT FROM AUTHOR]

This paper focuses on the cardinality constrained mean-variance portfolio optimization, in which only a small number of assets are invested. We first treat the covariance matrix of asset returns as a diagonal matrix with a special matrix processing technique. Using the dual theory, we formulate the lower bound problem of the original problem as a max-min optimization. For the inner minimization problem with the cardinality constraint, we obtain its analytical solution for the portfolio weights. Then, the lower bound problem turns out to be a simple concave optimization with respect to the Lagrangian multipliers. Thus, the interval split method and the supergradient method are developed to solve it. Based on the precise lower bound, the depth-first branch and bound method are designed to find the global optimal investment selection strategy. Compared with other lower bounds and the current popular mixed integer programming solvers, such as CPLEX and SCIP, the numerical experiments show that our method has a high searching efficiency. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12101317, 12271071, and 11991024], the Natural Science Foundation of Jiangsu Province [Grant BK20200819], the Team Project of Innovation Leading Talent in Chongqing [Grant CQYC20210309536], the Contract System Project of Chongqing Talent Plan [Grant cstc2022ycjh-bgzxm0147], and the Philosophy and Social Science Fund of Education Department of Jiangsu Province [Grant 2020SJA0168]. K.F.C. Yiu is supported in part by the Research Grants Council of Hong Hong [Grant PolyU 15223419], the Hong Kong Polytechnic University [Grants 4-ZZPT and 1-WZ0E], and the Research Centre for Quantitative Finance [Grant 1-CE03]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0344) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0344). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In this paper, an optimal PID tuning method is proposed for a class of two-link manipulators. In particular, the control specifications of the manipulators are considered. By modeling the control specifications into state constraints, the optimal PID tuning problem is converted to an optimal parameters selection problem with state constraints. An exact penalty function based method is then utilized to handle the state constraints. The superior of the proposed method over an existing method is verified by carrying out an numerical example. [ABSTRACT FROM AUTHOR]

Optimal switching is a special class of optimal control problems for hybrid dynamic systems. In this paper, we consider the optimal switching problem of linear-quadratic switched systems. The aim is to design a suitable switching strategy with the constraint on the number of switchings so that the quadratical performance achieves the minimum value. This problem is difficult to be solved because of the tight coupling between the continuous switching time and the discrete switching sequence. In our method, we first divide this hybrid optimization problem into two subproblems. In each of them, only one type of variable is considered. Then, we develop a gradient-based method with the time-scaling transformation to process the optimal switching time problem and a branch and bound method based on a series of exact lower bounds to handle the optimal switching sequence problem, respectively. By solving these two subproblems alternatively, the optimal switching strategy satisfying the constraint on the number of switchings can be obtained. Numerical examples are given to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [18], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem. [ABSTRACT FROM AUTHOR]

In this paper, we establish some existence results for the solution of the generalized symmetric set-valued quasi-equilibrium problem (GSSQEP). The new forms of GSSQEP via improvement set and scalar generalized symmetric set-valued quasi-equilibrium problem (GSSQEP Δ for short) are also introduced. By using Kakutani–Fan–Glicksberg fixed point method, maximal element principle and nonlinear scalarization technique, we develop two classes of sufficient conditions for the existence of solutions to GSSQEP. The drawback of some existing work for this problem is overcome. Moreover, some applications to the symmetric set-valued equilibrium problem (SSEP), symmetric vector quasi-equilibrium problem (SVQEP) and the set-valued equilibrium problem (SEP) are also given in this paper. Our results improve a few existing ones in Fakhar and Zafarani [Generalized symmetric vector quasiequilibrium problems. J Optim Theory Appl. 2008;136:397–409], Farajzadeh et al. [On the existence of solutions of symmetric vector equilibrium problems via nonlinear scalarization. Bull Iran Math Soc. 2019;45:35–58], Fu [Symmetric vector quasi-equilibrium problems. J Math Anal Appl. 2003;285:708–713], Han et al. [Existence of solutions for symmetric vector set-valued quasi-equilibrium problems with applications. Pacific J Optim. 2018;14:31–49]. [ABSTRACT FROM AUTHOR]

This article introduces a new autoregressive stochastic volatility (SV) model with a new piecewise linear structure such that the regime‐switching mechanism has a buffer zone where regime‐switching is delayed. The proposed model allows us to model the hysteretic phenomenon of the regime‐switching existing on both the mean equation and the volatility equation. A full description of the proposed Markov chain Monte Carlo method is given. In the empirical study, we consider the daily closing prices of NIKKEI stock average, the exchange rate for US Dollar to Japanese Yen and Hang Seng Index. Deviance information criterion measure shows that our proposed model outperforms the classical threshold SV models. [ABSTRACT FROM AUTHOR]

This paper investigates the mean-field stochastic linear quadratic optimal control problem of Markov regime switching system (M-MF-SLQ, for short). The representation of the cost functional for the M-MF-SLQ is derived using the technique of operators. It is shown that the convexity of the cost functional is necessary for the finiteness of the M-MF-SLQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. We demonstrate with a few examples that our results can be employed for tackling some financial problems such as mean-variance portfolio selection problem. [ABSTRACT FROM AUTHOR]

This paper aims to study the stability of a class of semi-infinite vector optimization problems (SVOP) under functional perturbations. By using an important hypothesis H h (p 0) , a necessary and sufficient condition of Hausdorff continuity for weak efficient solution mappings and certain sufficient conditions for Painlevé-Kuratowski convergence of weak efficient solution sets for SVOP are established under the perturbations of both constraint sets and objective functions. [ABSTRACT FROM AUTHOR]

This paper studies the portfolio management problem for an individual with a non-exponential discount function and habit formation in finite time. The investor receives a deterministic income, invests in risky assets, buys insurance and consumes continuously. The objective is to maximize the utility of excessive consumption, heritage and terminal wealth. The non-exponential discounting makes the optimal strategy adopted by a naive person time-inconsistent. The equilibrium for a sophisticated person is Nash subgame perfect equilibrium, and the sophisticated person is time-consistent. We calculate the analytical solution for both the naive strategy and equilibrium strategy in the CRRA case and compare the results of the two strategies. By numerical simulation, we find that the sophisticated individual will spend less on consumption and insurance and save more than the naive person. The difference in the strategies of the naive and sophisticated person decreases over time. Furthermore, if an individual of either type is more patient in the future or has a greater tendency toward habit formation, he/she will consume less and buy less insurance, and the degree of inconsistency will also be increased. The sophisticated person's consumption and habit level are initially lower than those of a naive person but are higher in later periods. [ABSTRACT FROM AUTHOR]