arXiv subjects

Krzysztof Kȩpczyński

Publications and source records attributed to Krzysztof Kȩpczyński.

2 recordsLinked to original sources

arXiv2020

Running supremum of Brownian motion in dimension 2: exact and asymptotic results

This paper investigates $π_T(a_1,a_2) = \mathbb{P}\left(\sup\limits_{t\in[0,T]} (σ_1B(t)-c_1t)>a_1, \sup\limits_{t\in[0,T]}( σ_2 B(t)-c_2t)>a_2\right),$ where $\{B(t) : t \geq 0\}$ is a standard Brownian motion, with $T >0, σ_1,σ_2>0, c_1, c_2\in\mathbb{R}.$ We derive explicit formula for the probability $π_T\left(a_1,a_2\right)$ and find its asymptotic behavior both in the so called many-source and high-threshold regimes.

math.PR↗

arXiv2020

Proportional reinsurance for fractional Brownian risk model

This paper investigates ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. We focus on joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of both insurance and reinsurance companies are composed of a large number of i.i.d. sub-risk processes, representing independent businesses. We derive the asymptotics as the initial capital tends to infinity.

math.PR↗