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Non-Markovian Impulse Control Under Nonlinear Expectation
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-3111-4820
2023 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 88, no 3, article id 72Article in journal (Refereed) Published
Abstract [en]

We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper and lower value functions satisfy a dynamic programming principle (DPP). We first prove the dynamic programming principle (DPP) for a truncated version of the upper value function in a straightforward manner. Relying on a uniform convergence argument then enables us to show the DPP for the general setting. Following this, we use an approximation based on a combination of truncation and discretization to show that the upper and lower value functions coincide, thus establishing that the game has a value and that the DPP holds for the lower value function as well. Finally, we show that the DPP admits a unique solution and give conditions under which a saddle point for the game exists. As an example, we consider a stochastic differential game (SDG) of impulse versus classical control of path-dependent stochastic differential equations (SDEs).

Place, publisher, year, edition, pages
Springer, 2023. Vol. 88, no 3, article id 72
Keywords [en]
Impulse control, Non-linear expectation, Risk-sensitivity, Stochastic differential games, Zero-sum games
National Category
Control Engineering
Research subject
Physics, Electrotechnology
Identifiers
URN: urn:nbn:se:lnu:diva-124129DOI: 10.1007/s00245-023-10049-7ISI: 001050460600004Scopus ID: 2-s2.0-85168414639OAI: oai:DiVA.org:lnu-124129DiVA, id: diva2:1795536
Available from: 2023-09-08 Created: 2023-09-08 Last updated: 2023-10-11Bibliographically approved

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Perninge, Magnus

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