On the value of non-Markovian Dynkin games with partial and asymmetric information
| Autor: | De Angelis, T, Merkulov, N, Palczewski, J |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Computer Science::Computer Science and Game Theory Probability (math.PR) partial information Mathematical Finance (q-fin.MF) FOS: Economics and business randomised stopping times regular processes optimal stopping Optimization and Control (math.OC) Quantitative Finance - Mathematical Finance asymmetric information FOS: Mathematics Non-Markovian Dynkin games Statistics Probability and Uncertainty predictable-jump processes Mathematics - Optimization and Control Mathematics - Probability 91A27 91A55 91A15 60G07 60G40 |
| Zdroj: | The Annals of Applied Probability. 32 |
| ISSN: | 1050-5164 |
| DOI: | 10.1214/21-aap1721 |
| Popis: | We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of our method of proof we also obtain existence of optimal strategies for both players. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyond the variational methods (based on PDEs) developed in the literature on Dynkin games in continuous time with partial/asymmetric information. Instead, we focus on a probabilistic and functional analytic approach based on the general theory of stochastic processes and Sion's min-max theorem (M. Sion, Pacific J. Math., 8, 1958, pp. 171-176). Our framework encompasses examples found in the literature on continuous time Dynkin games with asymmetric information and we provide counterexamples to show that our assumptions cannot be further relaxed. Changes include the proof of existence of a saddle point for the game and inclusion of a separate payoff when players stop at the same time. There are also some editorial changes and improvements in presentation |
| Databáze: | OpenAIRE |
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