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On the joint survival probability of two collaborating firms

Part of: Existence theories Miscellaneous topics - Partial differential equations Mathematical economics

Published online by Cambridge University Press:  01 August 2023

Stefan Ankirchner ,
Robert Hesse  and
Maike Klein
Stefan Ankirchner*
Affiliation:
Friedrich Schiller University Jena
Robert Hesse*
Affiliation:
Friedrich Schiller University Jena
Maike Klein*
Affiliation:
Kiel University
*
*Postal address: Ernst-Abbe-Platz 2, 07743 Jena, Germany.
*Postal address: Ernst-Abbe-Platz 2, 07743 Jena, Germany.
****Postal address: Heinrich-Hecht-Platz 6, 24118 Kiel, Germany. Email address: maike.klein@math.uni-kiel.de
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Abstract

We consider the problem of controlling the drift and diffusion rate of the endowment processes of two firms such that the joint survival probability is maximized. We assume that the endowment processes are continuous diffusions, driven by independent Brownian motions, and that the aggregate endowment is a Brownian motion with constant drift and diffusion rate. Our results reveal that the maximal joint survival probability depends only on the aggregate risk-adjusted return and on the maximal risk-adjusted return that can be implemented in each firm. Here the risk-adjusted return is understood as the drift rate divided by the squared diffusion rate.

Keywords

Ruin probabilityoptimal controltwo-dimensional Brownian motion

MSC classification

Primary: 49J20: Optimal control problems involving partial differential equations 35R35: Free boundary problems
Secondary: 91B70: Stochastic models
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 16
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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