<div class="csl-bib-body">
<div class="csl-entry">Grandits, P. (2025). A singularly perturbed ruin problem for a two-dimensional Brownian motion in the positive quadrant. <i>Journal of Applied Probability</i>, <i>62</i>(1), 269–283. https://doi.org/10.1017/jpr.2024.68</div>
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dc.identifier.issn
0021-9002
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/222772
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dc.description.abstract
We consider the following problem: the drift of the wealth process of two companies, modelled by a two-dimensional Brownian motion, is controllable such that the total drift adds up to a constant. The aim is to maximize the probability that both companies survive. We assume that the volatility of one company is small with respect to the other, and use methods from singular perturbation theory to construct a formal approximation of the value function. Moreover, we validate this formal result by explicitly constructing a strategy that provides a target functional, approximating the value function uniformly on the whole state space.
en
dc.language.iso
en
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dc.publisher
CAMBRIDGE UNIV PRESS
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dc.relation.ispartof
Journal of Applied Probability
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dc.subject
free boundary problem
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dc.subject
optimal control problem
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dc.subject
Ruin probability
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dc.subject
singular perturbation
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dc.title
A singularly perturbed ruin problem for a two-dimensional Brownian motion in the positive quadrant
