Next Article in Journal
Parametric Conditions of High Financial Risk in the SME Sector
Next Article in Special Issue
Potential Densities for Taxed Spectrally Negative Lévy Risk Processes
Previous Article in Journal
Loss Reserving Models: Granular and Machine Learning Forms
Previous Article in Special Issue
De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes
Open AccessArticle

Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model

by Krzysztof Dȩbicki 1,†, Lanpeng Ji 2,* and Tomasz Rolski 1,†
1
Mathematical Institute, University of Wrocław, 50-137 Wrocław, Poland
2
School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Risks 2019, 7(3), 83; https://doi.org/10.3390/risks7030083
Received: 14 June 2019 / Revised: 19 July 2019 / Accepted: 29 July 2019 / Published: 1 August 2019
We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function P ( u ) for the component-wise ruin (that is both business lines are ruined in an infinite-time horizon), where u is the same initial capital for each line. We measure the goodness of the business by analysing the adjustment coefficient, that is the limit of ln P ( u ) / u as u tends to infinity, which depends essentially on the correlation ρ of the two surplus processes. In order to work out the adjustment coefficient we solve a two-layer optimization problem. View Full-Text
Keywords: adjustment coefficient; logarithmic asymptotics; quadratic programming problem; ruin probability; two-dimensional Brownian motion adjustment coefficient; logarithmic asymptotics; quadratic programming problem; ruin probability; two-dimensional Brownian motion
Show Figures

Figure 1

MDPI and ACS Style

Dȩbicki, K.; Ji, L.; Rolski, T. Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model. Risks 2019, 7, 83.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop