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Maximum Principle for McKean-Vlasov Dynamic Using Lions Partial-Derivatives with Respect to Probability with Application to Finance | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 2، مهر 2026، صفحه 63-76 اصل مقاله (505.85 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.89775.1241 | ||
| نویسندگان | ||
| Ikram Hamed* 1؛ Noureddine Hamed2؛ Messaouda Terchi3 | ||
| 1Department of Mathematics, University Mohamed Khider of Biskra, Po. Box 145, 07000 Biskra. | ||
| 2Jouf University, Kingdom of Saudi Arabia KSA. | ||
| 3Laboratory of Science for Mathematics, Computer Science and Engineering Applications, Department of Mathematics, Institute of Science, University Center of Barika. Algeria | ||
| چکیده | ||
| In this paper, we study optimal control problem for stochastic systems generated by general McKean-Vlasov dynamics. The coefficients of the McKean-Vlasov dynamic depend on the state of the solution process as well as of its probability law. The information available to the controller is possibly less than the whole information. Our necessary maximum principle is established by applying Girsanov's Lemma and Lions's partial-derivatives with respect to probability law. As an application to finance, the conditional random mean-variance portfolio selection problem of McKean-Vlasov type is discussed to illustrate our theoretical results, where the optimal partially observed portfolio has been derived explicitly. | ||
| کلیدواژهها | ||
| McKean-Vlasov stochastic systems؛ Stochastic optimal control؛ Probability and stochastic process؛ Markowitz portfolio theory؛ Girsanov Lemma؛ Finance models | ||
| مراجع | ||
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