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In this study, we model aggregate claims using a subordinator, specifically a non-decreasing Lévy process. Large positive jumps, exceeding a predetermined threshold, represent significant claims, while frequent but smaller fluctuations capture other sources of non-insurance uncertainty, such as miscellaneous expenses. The primary challenge lies in extracting the necessary mathematical insights to estimate the jump measure from a sample path of truncated aggregate claims. Through a discrete time-point sampling scheme, we conduct an initial comparison between conventional parametric estimators of the Lévy measure associated with the subordinator, based on simulated significant claims, and our proposed non-parametric estimator, derived by adapting classical differential processes originally introduced by Rubin and Tucker. The results of this comparison suggest the potential utility of our estimator in the context of real data from the insurance sector. While the primary focus of this work is to uncover the mathematical foundations, a preliminary simulation study, although lacking rigorous numerical analysis, hints at the favorable estimation of the Poisson rate for the number of jumps exceeding the threshold, achieved using our proposed non-parametric estimator of the Lévy measure. [ABSTRACT FROM AUTHOR]

Abstract.The data distributions of many financial and econometric sequences always exhibit heavy-tailed phenomena, which trigger distinct difficulty in parameter estimation by classical least squares method. This article aims to construct a new ratio-typed test based on least absolute deviation estimation that effectively circumvents the problem of long-run variance estimation and has robustness on detecting structural changes under strong mixing sequences with heavy-tailed innovations. This is because the least absolute deviation estimation can allow for processes within the domain of attraction of a stable law with an index κ∈(0,2), not limited to (1, 2). Under some regular conditions, the asymptotic distribution under the null hypothesis is derived as a functional of Brownian motion, not a functional of lévy process, and the divergence rate under the alternative hypothesis is also provided. Furthermore, the consistency of a ratio-typed change point estimator is given and its convergence rate is established. The numerical simulation indicates that empirical sizes are undistorted, and empirical powers exhibit significant performance. Finally, two practical application examples are presented to illustrate the validity of the proposed test procedures. [ABSTRACT FROM AUTHOR]

To achieve the optimal solution between construction costs and carbon emissions in the multi-target optimization scheduling, this paper proposes a multi-objective optimization scheduling design for wind–solar energy storage microgrids based on an improved oppositional gradient grey wolf optimization (OGGWO) algorithm. First, two new features were added to the traditional grey wolf optimization (GWO) algorithm to solve the multi-target optimization scheduling of grid-connected microgrids, aiming to improve solution quality and convergence speed. Furthermore, Gaussian walk and Lévy flight are introduced to enhance the search capability of the proposed OGGWO algorithm. This method expands the search range while sacrificing only a small amount of search speed, contributing to obtaining the global optimal solution. Finally, the gradient direction is considered in the feature search process, allowing for a comprehensive understanding of the search space, which facilitates achieving the global optimum. Experimental results indicate that, compared to traditional methods, the proposed improved OGGWO algorithm can achieve standard deviations of 4.88 and 4.46 in two different scenarios, demonstrating significant effectiveness in reducing costs and pollution. [ABSTRACT FROM AUTHOR]

In order to solve the problem of poor adaptability and robustness of the rule-based energy management strategy (EMS) in hybrid commercial vehicles, leading to suboptimal vehicle economy, this paper proposes an improved dung beetle algorithm (DBO) optimized multi-fuzzy control EMS. First, the rule-based EMS is established by dividing the efficient working areas of the methanol engine and power battery. The Tent chaotic mapping is then used to integrate strategies of cosine, Lévy flight, and Cauchy Gaussian mutation, improving the DBO. This integration compensates for the traditional dung beetle algorithm's tendency to fall into local optima and enhances its global search capability. Subsequently, fuzzy controllers for the driving charging mode and hybrid driving mode are designed under this rule-based EMS. Finally, the improved DBO is used to obtain the optimal control of the fuzzy controller by taking the fuel consumption of the whole vehicle and the fluctuation change of the battery state of charge (SOC) as the optimization objectives. Compared to traditional rule-based energy management strategies, the optimized fuzzy control using the enhanced DBO continuously adjusts the torque distribution between the engine and motor based on the vehicle's real-time state, resulting in a 9.07% reduction in fuel consumption and a 3.43% decrease in battery SOC fluctuations. [ABSTRACT FROM AUTHOR]

In the framework of contemporary power systems, a distributed generation (DG) system has benefits, but it also presents several operational challenges. In a networked distributed generation system, islanding is one such problem. Because of the negative consequences, an islanding event should be distinguished from other events, like transients within the minimum time. A multi-level adaptive neuro-fuzzy inference system (ANFIS) is being developed in this work to effectively detect islanding. To train the ANFIS model, a novel hybrid scheme based on Lévy flights and teaching–learning-based optimiser is suggested. The performance of the developed algorithm is evaluated using the IEEE CEC-C06 and other traditional benchmark functions. The ANFIS model's classification regime is significantly improved by the optimisation algorithm. In the test system, renewable energy sources are used to power a voltage source converter unit in a network-forming mode via an energy storage medium. Based on measured frequency, RMS voltage and current, active and reactive power, voltage, and current THD at the point of common coupling (PCC), the trained ANFIS controller deduces the islanding detection command to the circuit breaker. The plan is verified following the UL1741 standard for islanding prevention, yielding notable outcomes with an average detection time of 0.04s and an accuracy of 89.3%. [ABSTRACT FROM AUTHOR]

We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable Lévy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of Ornstein-Uhlenbeck processes. However, unlike Ornstein-Uhlenbeck processes with a tempered stable driver exact transition probabilities for higher order CARMA processes are not explicitly given. Therefore, we use a numerical sample path generation method and approximate the driving tempered stable Lévy process by a truncated series representations. We derive a result of a series representation for p-tempered α-stable distributions. We prove approximation error bounds and conduct Monte Carlo experiments to illustrate the usefulness of the approach. [ABSTRACT FROM AUTHOR]

We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures the market expectations of future volatility, but traditional methods based on second-moment shocks and the time-varying volatility of the VIX often do not effectively to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we constructed a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Lévy process to S&P 500 log returns, to provide a more comprehensive measure of volatility that captures the extreme movements and heavy tails observed in financial data. Using an axiomatic framework, we developed a family of risk–reward ratios that, when computed with our revised VIX and fitted to a long-memory time series model, provide a more precise identification of uncertainty shocks in financial markets. [ABSTRACT FROM AUTHOR]

Structural credit risk modeling is a commonly used risk-management approach for fixed-income, with Lévy models offering more realistic tail behavior than assumed in the classical Merton formulation. This article presents an innovative Esscher-based algorithm for computing default probabilities in structural credit risk models driven by Lévy processes. The algorithm starts by matching the moments of observed equity values to infer model parameters. Using the cumulant generating function, it then computes the risk-neutral characteristic function and derives asset values through inversion of a Fourier option pricing formula. The physical parameters are updated by matching the moments of these asset values, iterating until convergence. As an illustration, the algorithm is applied to multiple issuers with various ratings, and to three Lévy models: Merton, variance gamma, and bilateral gamma. As expected, the Merton model consistently underestimates default probabilities for short maturities; the bilateral gamma model provides more conservative estimates. The empirical analysis demonstrates the robustness of the algorithm across different market conditions, highlighting its ability to provide valuable insights for both academic research and practical risk management. This approach, therefore, offers a complimentary risk-modeling perspective to the traditional Merton framework. For reader's convenience, calibration code is made publicly available. [ABSTRACT FROM AUTHOR]

Robotic mixed-model assembly line (RMAL) is challenged to achieve double win for productivity and energy savings in the manufacturing industry. Joint balancing and sequencing is an effective method to enhance the productivity and intelligent collaboration capabilities of RMAL. The energy-saving strategy contributes deeply to reducing energy consumption of RMAL since it is attributed to energy-intensive industry. This study investigates joint balancing and sequencing problem for Type-II RMAL (RMALBSP-II) considering energy consumption. A novel bi-objective model with minimizing the maximum completion time and energy consumption is constructed to achieve joint decision-making and double win objectives for RMALBSP-II. Particularly, production changeover setup is innovatively considered in the model, and robot shutdown strategy is formulated to save energy consumption under the robot’s idle state. To solve the model, a new Multi-objective Discrete Hybrid Cuckoo Search Algorithm (MDHCSA) is explored, and a neighborhood search is used instead of Lévy flight to achieve the search for the discrete optimal solution. Besides, mutation operations within NSGA-II and a new initialization method for task assignment are introduced to improve algorithm performance. Extensive numerical experiments show that the shutdown strategy can save energy and considering the impact of product switching setup can achieve energy saving and efficiency improvement. In addition, the proposed MDHCSA algorithm outperforms other popular multi-objective algorithms. [ABSTRACT FROM AUTHOR]

• A lévy flight and chaotic local Search-based discrete mayfly algorithm is proposed. • The exploration and exploitation capabilities and local and global optimizations of the traditional algorithm have been improved. • The algorithm solved the precautionary maintenance-planning problem in power generation systems. An adequate and reliable precautionary upkeep plan in power generation systems is required to reduce failures, to improve the generator's lifespan, to diminish repair costs and to ensure consistent power supply to consumers with managing the energy flows in power systems. The Generators' Precautionary Upkeep Planning (GPUP) problem is a complex optimization problem. It is a critical challenge in the power generation industry, involving the optimization of maintenance schedules for power generators to minimize the generation reserve and maximize the reliability. This problem consists of several important restrictions which include the load power demand and the labour force restrictions. In this research paper, a Discrete Chaotic Mayfly Optimization (DCMFO) algorithm which uses Lévy flight random walk for female mayflies and chaotic local search move rule for male ones, is adapted for designing an appropriate precautionary upkeep scheme of a list of generators in power generation systems. The DCMFO algorithm is evaluated using 21-unit test thermal power system. The results indicate that unlike the classical DMFO algorithm, the DCMFO algorithm has proven to have superior optimization capabilities and to surpass all earlier adopted algorithms in performance. This reinforces DCMFO's standing as the current leading optimization algorithm for solving this particular problem, ever since its initial inception. The DCMFO's efficiency and reliability have been demonstrated with different cases through several statistical tests. [ABSTRACT FROM AUTHOR]