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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 4, Pages 811–823
DOI: https://doi.org/10.4213/tvp5276 (Mi tvp5276) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

A ruin problem for a two-dimensional Brownian motion with controllable drift in the positive quadrant

P. Grandits

Institut für Stochastik und Wirtschaftsmathematik, Technische Universität Wien, Wien, Austria
Full-text PDF (459 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp5276
Abstract: In this paper a two-dimensional Brownian motion (modeling the endowment of two companies), absorbed at the boundary of the positive quadrant, with controlled drift, is considered. We allow that both drifts add up to the maximal value of one. Our target is to choose the strategy in a way s.t. the expected value of the number of surviving companies is maximized. The optimal strategy for this problem is investigated, and it is shown rigorously that the strategy of always pushing maximally the company with less endowment—a strategy which is optimal in the case when one wants to maximize the probability that both companies survive—is in fact not optimal.
Keywords: ruin probabilities, optimal control problem, atlas model, free boundary problems.
Funding agency Grant number
Austrian Science Fund P30864-N35
This work was supported by the “Austrian Science Foundation” (Fonds zur Förderung der Wissenschaftlichen Forschung) (project P30864-N35).
Received: 19.09.2016
Revised: 10.01.2019
Accepted: 12.02.2019
English version:
Theory of Probability and its Applications, 2020, Volume 64, Issue 4, Pages 646–655
DOI: https://doi.org/10.1137/S0040585X97T989763
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. Grandits, “A ruin problem for a two-dimensional Brownian motion with controllable drift in the positive quadrant”, Teor. Veroyatnost. i Primenen., 64:4 (2019), 811–823; Theory Probab. Appl., 64:4 (2020), 646–655
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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