Stochastic Differential Games and Optimization Problems with Controlled Point Process Arrivals
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10957_2025_Article_2690.pdf
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Author(s)
Wernerfelt, Birger
Date Issued
May 30, 2025
Journal
Journal of Optimization Theory and Applications
Publisher
Springer US
Citation
Wernerfelt, B. Stochastic Differential Games and Optimization Problems with Controlled Point Process Arrivals. J Optim Theory Appl 206, 42 (2025).
Version
Final published version
Abstract
There is a very large literature on applications of stochastic control of jump diffusions and a smaller literature on such games. In many applications it is natural to assume that the arrival intensity is controlled, but except for two long-forgotten papers the literature instead assumes that it is the jump sizes that are controlled. The more natural assumption is typically avoided because a failed Lipschitz condition means that the classical existence and uniqueness proofs cannot be used. We here derive an asymptotic Markov equilibrium of the game with controlled jump intensities and show that it, at least in an example, is very similar to the Markov equilibrium of an analog game with controlled jump sizes. The paper thus makes two contributions: It supplies a way to solve some optimization problems and games with controlled jump intensities and it shows that the commonly used formulation with controlled jump sizes is quite defensible for at least some classes of games.
MIT Department
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1007/s10957-025-02690-9
