American options with asymmetric information and reflected BSDE

Esmaeeli, Neda; Imkeller, Peter

doi:10.3150/16-bej902

Cited by 9 publications

(4 citation statements)

References 33 publications

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“…By construction of R n and R, this proves convergence of R n T to R T . Then, the processes R n and R fulfil all the assumptions of Proposition 5.10 whose application allows us to obtain (20).…”

Section: Technical Resultsmentioning

confidence: 92%

“…The observation flows for the players are given by (F 1 t ) and (F 2 t ), respectively. The particular structure of players' filtrations (F 1 t ) and (F 2 t ) allows for the following decomposition of randomised stopping times, see [20,Proposition 3.3] (recall the radomisation devices Z τ ∼ U ([0, 1]) and Z σ ∼ U ([0, 1]), which are mutually independent and independent of F T ).…”

Section: Game With Partially Observed Scenariosmentioning

confidence: 99%

See 1 more Smart Citation

On the value of non-Markovian Dynkin games with partial and asymmetric information

De Angelis,

Merkulov,

Palczewski

2020

Preprint

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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 càdlàg measurable processes. 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 related 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.

show abstract

Section: Technical Resultsmentioning

confidence: 92%

Section: Game With Partially Observed Scenariosmentioning

confidence: 99%

On the value of non-Markovian Dynkin games with partial and asymmetric information

De Angelis,

Merkulov,

Palczewski

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…X t (ω)dρ t (ω), for P-a.e. ω ∈ Ω, then the result in (21) will follow by the dominated convergence theorem. By assumption there is Ω 0 ⊂ Ω with P(Ω 0 ) = 1 and such that ρ n t (ω) → ρ t (ω) at all points of continuity of t → ρ t (ω) and at the terminal time T for all ω ∈ Ω 0 .…”

Section: Technical Resultsmentioning

confidence: 99%

“…The observation flows for the players are given by (F 1 t ) and (F 2 t ), respectively. The particular structure of players' filtrations (F 1 t ) and (F 2 t ) allows for the following decomposition of randomised stopping times, see [21,Proposition 3.3] (recall the radomisation devices Z τ ∼ U ([0, 1]) and Z σ ∼ U ([0, 1]), which are mutually independent and independent of F T ).…”

mentioning

confidence: 99%

On the value of non-Markovian Dynkin games with partial and asymmetric information

2022

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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 càdlàg 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.

show abstract