Applied Stochastic Models in Business and Industry最新文献

Cyberspace is a dynamic ecosystem consisting of interconnected data, devices, and individuals, with multiple network layers comprising identifiable nodes. Location-based information can significantly improve cyber resilience decision-making and facilitate the development of innovative cyber risk pricing tools. This article is based on a methodology that uses company geospatial data to accurately estimate the number of expected losses arising from cyberattacks. Our approach aims to build and compare statistical spatial models that allow pricing cyber policies more effectively than traditional non-spatial methods by incorporating all available data. By accounting for spatial dependence, we can assess the risk of data breaches and contribute to the design of more efficient cyber risk policies for the insurance market.

In this paper we model the dynamics of the Chinese crude oil futures returns by using a skew-geometric Brownian motion correlated with the market volatility, which is taken as a square-root stochastic process. We use the OVX index data as proxy for market volatility. We validate the proposed model in terms of accuracy of its calibrations through an in-sample simulation. Instead, out-of-sample simulations are used to show that a correlated skew-geometric Brownian motion is more appropriate for modelling the Chinese returns compared to a single skew-geometric Brownian motion in terms of forecasts. Furthermore, we price an American call option on the Chinese futures by using a recursively scheme based on a closed-form formula, and an alternative Monte Carlo approach, for the related European call option. We show that our call price estimates are very close to market values and our model generally outperforms many benchmarks in literature, such as the Barone-Adesi and Whaley formula and its generalizations.

We propose a method called SVM-Jacobi to approximate probability distributions by linear combinations of exponential distributions, associated with a comprehensive asymptotic analysis. In multivariate cases, the multivariate distribution is approximated by linear combinations of products of independent exponential distributions, and the method works effectively. The proposed method has many applications in both quantitative finance and insurance, especially for modeling random time, like default time and remaining lifetime. In addition to the methodology and theoretical analysis, we provide examples of pricing defaultable bonds, European options, credit default swaps, equity-linked death benefits, and calculating the credit value adjustment of credit default swaps. Finally, some numerical results based on real data and simulated data are presented for illustration.

In this article, a new $��\delta �$-shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non-critical shock occurs in a time length less than $��{�\delta �}_{�1�}�$ or a shock after a critical shock occurs in a time length less than $��{�\delta �}_{�2�}�,�$ where . The distribution of the system's lifetime is studied for both discrete and continuous intershock time distributions. It is shown that a new model is useful to describe a certain cold standby repairable system.

This article focuses on the correlation between the degradation levels of the two components that form a system. The degradation evolution of each component is modeled using Wiener processes. Both components are dependent and this dependence is described using the trivariate reduction method. To reduce the degradation and extend the system lifetime, preventive maintenance actions are periodically performed. These preventive maintenance actions are imperfect and they are modeled by using an arithmetic reduction of degradation of infinite order model with a determined maintenance efficiency parameter. The evolution of the maintained system is analysed by assessing the expectation and variance of both degradation processes at successive maintenance times. The novelty of this work is the analysis of the Pearson correlation coefficient between the degradation levels of the two components. Different properties of the monotonicity of the Pearson correlation coefficient between the two degradation paths are obtained by considering equal maintenance efficiency and equal general time scales functions for the two Wiener degradation processes associated to each degrading component.

In this article, we aim to provide a detailed econometric analysis of the realized volatility in international stock markets of Brazil, China, Europe, India, the United Kingdom, and the United States, which represent a mix of large developing, and developed markets. For our purpose, we use the functional data analysis (FDA) framework, whence discrete volatility data were first transformed into continuous functions, and thereafter, derivatives of the continuous functions were investigated, and kinetic and potential energy associated is the volatility system were extracted. Results revealed that COVID-19 indeed had a significant effect on international financial market volatility for all the countries, with the exception of China. The realized volatility of the international financial markets did return to their pre-COVID levels in May 2020, and this recovery time was significantly faster than the 2008 financial crisis recovery period. Within the FDA framework, we further investigated the role of uncertainty on the realized volatility, specifically from an outbreak of an infectious disease (such as COVID-19) and a daily newspaper-based infectious disease index as the predictor. The regression analysis showed that the volatility of financial markets can be accurately modeled by this infectious disease index, but only for periods experiencing an epidemic or pandemic.

Accelerated degradation tests (ADTs) are widely used for assessing the reliability of long-life products. During an ADT, accelerated stresses not only expedite the degradation of test products but also increase the likelihood of encountering traumatic shocks. Moreover, it is important to acknowledge that measurement errors can be inevitable during the observation process of an ADT. Unfortunately, these errors are often overlooked in the optimal design of the ADT, especially when multiple competing failure modes are present. In this article, we propose a new approach to design ADTs when measurement errors exist and test products suffer from degradation failures and random shock failures. We utilize the Wiener process to model the degradation path, incorporating normally distributed measurement errors, and an exponential distribution to fit the time between random shock failures. Given the number of test products and the termination time, we optimize the ADT plans under three common design criteria. The equivalence theorem is used to verify the optimality of the optimal ADT plans. A real-life example and sensitivity analysis are provided to illustrate our proposed method. The results demonstrate that when competing failure modes are present, the optimal ADT plans, which account for measurement errors, differ significantly from those that do not consider such errors.