Max-stable random fields; Chaos of random fields; Ruin time approximation; Levy processes; Gaussian random fields; Exit probabilties; Rare events and extremes ; Storage process; Ruin probabilities; Threshold-dependent random field; Pickands type constants; Queueing theory; Risk theory
Deng Pingjin (2018), The Joint Distribution of Running Maximum of a Slepian Process, in
Methodology and Computing in Applied Probability, 20(4), 1123-1135.
Bai Long, Dȩbicki Krzysztof, Hashorva Enkelejd, Ji Lanpeng (2018), Extremes of threshold-dependent Gaussian processes, in
Science China Mathematics, 61(11), 1971-2002.
Hashorva E.nkelejd (2018), Representations of max-stable processes via exponential tilting, in
Stochastic Processes Applications, 128(9), 2952-2978.
Bai L. (2018), Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon, in
Scandinavian Actuarial Journal, (6), 514-528.
Hashorva E., Ratomovirija G., Tamraz M., Bai Y. (2018), Some Mathematical Aspects of Price Optimisation, in
Scandinavian Actuarial Journal, (5), 379-403.
Bai L., Debicki K., Hashorva E., Luo L. (2018), On Generalised Piterbarg Constants, in
Methodology and Computing in Applied Probability, 20(1), 137-164.
А. И. Жданов, В. И. Питербар (2018), Большие выбросы процессов гауссовского хаоса. Аппроксимация в дискретном времени, in
Теория вероятн. и ее примен, 63(1), 3-28.
Hashorva E., Seleznjev O, Tan Z. (2018), Approximation of Maximum of Gaussian Random Fields, in
Journal of Mathematical Analysis Applications, 457(1), 841-867.
Debicki K, Farkas J., Hashorva E. (2018), Extremes of Randomly Scaled Gumbel Risks, in
Journal of Mathematical Analysis Applications, 458(1), 30-42.
Debicki K., Hashorva E., Ji L., Ling C. (2017), Comparison Inequalities for Order Statistics of Gaussian Arrays, in
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 14(1), 93-116.
Farkas Julia, Hashorva Enkelejd, Piterbarg Vladimir I. (2017),
Asymptotic Behavior of Reliability Function for Multidimensional Aggregated Weibull Type Reliability Indices: Analytical and Computational Methods in Probability Theory, Springer International Publishing, Cham.
Debicki K, Hashorva E., Liu P. (2017), Extremes of gamma-reflected Gaussian processes with stationary increments, in
ESAIM: Probability and Statistics, 21, 495-535.
Debicki K., Hashorva E. (2017), On extremal index of max-stable processes, in
Probability and Mathematical Statistics, 37(2), 299-317.
Asmussen S., Hashorva E., Laub P, Taimre T (2017), Tail Asymptotics of Light -tailed Weibull-like Sums, in
Probability and Mathematical Statistics, 37(2), 235-256.
Debicki K., Hashorva E., Liu P. (2017), Uniform Tail Approximation of homogenous functionals of Gaussian fields, in
Advances Applied Probability, 49(4), 1037-1066.
Hashorva E, Ratovomirija G., Tamraz M. (2017), On some new dependence models derived from multivariate collective models in insurance applications, in
Scandinavian Actuarial Journal, 2017(8), 730-750.
Debicki K., Hashorva E., Liu P. (2017), Extremes of Gaussian random fields with regularly varying dependence structure, in
Extremes, 20, 333-392.
Deng PingJin (2017), The boundary non-crossing probabilities for Slepian process, in
Stat. Probab. Letters, 122, 26-35.
Liu Peng, Zhang Chunsheng, Ji Lanpeng (2017), A note on ruin problems in perturbed classical risk models, in
Statistics & Probability Letters, 120, 28-33.
Liu P., Ji L. (2017), Extremes of locally stationary chi-square processes with trend, in
Stoch Proc. Applications, 127, 497-525.
Bai Long (2017), Extremes of α(t)-locally stationary Gaussian processes with non-constant variances, in
Journal mathematical analysis and applications, 446, 248-263.
Peng X, Luo Li (2017), Finite time Parisian ruin of an integrated Gaussian risk model, in
Statistics & Probability Letters, 124, 22-29.
Debicki K, Engelke S., Hashorva E. (2017), Generalized Pickands constants and stationary max-stable processes, in
Extremes, 20, 493-517.
Debicki K, Liu P (2017), Lévy-driven GPS queues with heavy-tailed input, in
Queueing Systems, 85, 249-267.
Bai Long, Luo Li (2017), Parisian ruin of the brownian motion risk model with constant force of interest, in
Statistics and Probability Letters, 120, 34-44.
Albin J.M.P., Hashorva E., Ji L, Ling C (2016), Extremes and limit theorems for difference of chi-type processes, in
ESAIM Statistics & Probability, 20, 349-366.
Classical probabilistic models of risk theory are concerned with the analysis of ruin probabilities and the time of ruin of insurance portfolios. Similar models appear in queuing theory, financial mathematics and statistics. Due to the huge complexity of those models, current research and its applications are often concerned with asymptotic approximations of various quantities of interest. For instance, ruin probabilities are approximated and thus analysed by allowing the initial capital to grow to infinity. Previous research has shown that advanced models of risk and queueing theory can be addressed in the context of the asymptotic theory by introducing threshold-dependent random fields. Explained in the context of the approximation of ruin probabilities, this means that the imposed growth of the initial capital implies changes on the underlying risk model itself. Here the initial capital plays the role of the threshold. Indeed, threshold-dependent random processes and fields are encountered in numerous problems of mathematical statistics, finance and other research fields. The current literature offers few ad hoc techniques and tools for the study of extremes of threshold-dependent random fields, commonly assumed to be Gaussian. Therefore, the main objective of this project is to further develop the asymptotic theory of extremes of threshold-dependent random fields by considering also tractable non-Gaussian random fields. The developed theory will then be applied to several open problems of risk theory, queueing theory and mathematical statistics. We plan also to fill some gaps in the current literature concerned with extremes of processes with trend. In our findings the so-called Pickands-type constants will appear, which can be calculated by simulations. This project shall investigate in detail several Pickands-type constants by studying certain hidden connections with extreme value theory of max-stable random fields. The envisaged results are of great theoretical importance and can be used for efficient simulations of those unknown constants. In addition to numerous theoretical results and their interpretation, this project shall develop new techniques and extensions that are of interest in various applications of asymptotic theory and extreme value theory.