Applied Probability Society Student Paper Competition: Abstracts of 2019 Finalists

The journal is pleased to publish the abstracts of the winner and finalists of the 2019 Applied Probability Society’s student paper competition. The 2019 student paper prize committee was chaired by Amy Ward. The 2019 committee members are (in alphabetical order by last name): Reza Aghajani, Pelin Canbolat, Jing Dong, Johan van Leeuwaarden, Ilya Ryzhov, Assaf Zeevi, Jiheng Zhang, and Serhan Ziya.

Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments

In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for E((Snξ)α1(Snξ > x)) and E((Snξ – x)+)α, where α is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks.

Star-shaped order for distributions characterized by several parameters and some applications

The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.

Pandemic-type failures in multivariate Brownian risk models

Modelling of multiple simultaneous failures in insurance, finance and other areas of applied probability is important especially from the point of view of pandemic-type events. A benchmark limiting model for the analysis of multiple failures is the classical d-dimensional Brownian risk model (Brm), see Delsing et al. (Methodol. Comput. Appl. Probab. 22(3), 927–948 2020). From both theoretical and practical point of view, of interest is the calculation of the probability of multiple simultaneous failures in a given time horizon. The main findings of this contribution concern the approximation of the probability that at least k out of d components of Brm fail simultaneously. We derive both sharp bounds and asymptotic approximations of the probability of interest for the finite and the infinite time horizon. Our results extend previous findings of Dȩbicki et al. (J. Appl. Probab. 57(2), 597–612 2020) and Dȩbicki et al. (Stoch. Proc. Appl. 128(12), 4171–4206 2018).

Applied Probability Society Student Paper Competition: Abstracts of 2020 Finalists

The journal is pleased to publish the abstracts of the winner and finalists of the 2020 Applied Probability Society’s student paper competition. The 2020 student paper prize committee was chaired by Amy Ward. The 2020 committee members are (in alphabetical order by last name): Alessandro Arlotto, Sayan Banerjee, Junfei Huang, Jefferson Huang, Rouba Ibrahim, Peter Jacko, Henry Lam, Nan Liu, Yunan Liu, Siva Theja Maguluri, Giang Nguyen, Mariana Olvera-Cravioto, Lerzan Örmeci, Erhun Özkan, Jamol Pender, Weina Wang, Amy Ward (chair), Linwei Xin, Kuang Xu, Galit Yom-Tov, Assaf Zeevi, Jiheng Zhang, Zeyu Zheng, Yuan Zhong, Enlu Zhou, and Serhan Ziya.

Occupation times of Lévy processes

In this paper, we give a complete and succinct proof that an explicit formula for the occupation time holds for all Lévy processes, which is important to the pricing problems of various occupation-time-related derivatives such as step options and corridor options. We construct a sequence of Lévy processes converging to a given Lévy process to obtain our conclusion. Besides financial applications, the mathematical results about occupation times of a Lévy process are of interest in applied probability.