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

Krzysztof Dȩbicki, Lanpeng Ji and Tomasz Rolski
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Krzysztof Dȩbicki: Mathematical Institute, University of Wrocław, 50-137 Wrocław, Poland
Lanpeng Ji: School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK
Tomasz Rolski: Mathematical Institute, University of Wrocław, 50-137 Wrocław, Poland

Risks, 2019, vol. 7, issue 3, 1-21

Abstract: 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.

Keywords: adjustment coefficient; logarithmic asymptotics; quadratic programming problem; ruin probability; two-dimensional Brownian motion (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
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