Distributional equations and the ruin problem for the Sparre Andersen model with investments

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Distributional equations and the ruin problem for the Sparre Andersen model with investments

Extremes. 2026. Vol. 29. P. 65–87.

Промыслов П. В., Kabanov Y., Лёгенький Д. В.

This note is an addendum to the work initiated by Eberlein, Kabanov, and Schmidt and developed further by Kabanov and Promyslov on the asymptotics of the ruin probabilities in the Sparre Andersen model with investments in a risky asset. Using more advanced methods of the implicit renewal theory, we provide complements to some results of the mentioned works.

Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited

Veretennikov A., Mathematics 2023 Vol. 11 No. 14 Article 3096

Polynomial recurrence bounds for a class of stochastic differential equations with a rotational symmetric gradient type drift and an additive Wiener process are established, as well as certain a priori moment inequalities for solutions. The key feature of this paper is that the approach does not use Lyapunov functions because it is not clear how ...

Added: July 16, 2026

Dynamical trap model for stimulus–response dynamics of human control

Lubashevsky I., Lubashevskiy V., Computer Research and Modeling 2024 Vol. 16 No. 1 P. 79–87

We present a novel model for the dynamical trap of the stimulus-response type that mimics human control over dynamic systems when the bounded capacity of human cognition is a crucial factor. Our focus lies on scenarios where the subject modulates a control variable in response to a certain stimulus. In this context, the bounded capacity ...

Added: February 25, 2024

Modelling the industrial production of electric and gas utilities through the CIR^3 model

Ceci C., Bufalo M., Orlando G., Mathematics and Financial Economics (Германия) 2024 P. 1–25

This work aims to extend previous research on how a trifactorial stochastic model, which we call CIR^3 mode, can be turned into a forecasting tool for energy time series. In particular, in this work, we intend to predict changes in the industrial production of electric and gas utilities. The model accounts for several stylized facts ...

Added: February 16, 2024

Astrospheres of Planet-Hosting Cool Stars and Beyond ⋅ When Modeling Meets Observations

Herbst K., Baalmann L., Bykov A. et al., Space Science Reviews 2022 Vol. 218 No. 4 Article 29

Thanks to dedicated long-term missions like Voyager and GOES over the past 50 years, much insight has been gained on the activity of our Sun, the solar wind, its interaction with the interstellar medium, and, thus, about the formation, the evolution, and the structure of the heliosphere. Additionally, with the help of multi-wavelength observations by ...

Added: October 27, 2022

Динамика приспособления в сетевой игре со стохастическими параметрами

Volkova O. N., Вологина Д. -., Korolev A. V., Математическая теория игр и ее приложения 2022 Т. 14 № 1 С. 21–48

Вводятся стохастические параметры в модели сетевых игр с производством и экстерналиями знаний, которая была сформулирована В. Матвеенко и А. Королевым и обобщает двухпериодную модель Ромера. Агенты различаются продуктивностью, имеющей детерминированную и винеровскую составляющие. Рассматривается динамика, которая возникает при объединении двух полных сетей. Получены явные выражения в форме броуновских случайных процессов. Проведен качественный анализ решения системы ...

Added: May 11, 2022

Solving linear parabolic rough partial differential equations

Bayer C., Belomestny D., Redmann M. et al., Journal of Mathematical Analysis and Applications 2020 Vol. 490 No. 1 Article 124236

We study linear rough partial differential equations in the setting of [Friz and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear parabolic partial differential equation driven by a deterministic rough path W of Hölder regularity α with 1/3 < α ≤ 1/2. Based on a stochastic representation of the solution of the rough partial differential equation, we propose a ...

Added: May 22, 2020