Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs

Grigorova, Miryana

doi:10.1080/17442508.2016.1166505

Cited by 15 publications

(11 citation statements)

References 30 publications

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“…For each τ ∈ T S,T , we set τ A := τ 1 A + T 1 A c . We have τ A ≥ S ′ a.s. By using the fact that S = S ′ a.s. on A, the fact that τ A = τ a.s. on A, and a standard property of conditional f -expectations (cf., e.g., Proposition A.3 in [19] which can be extended without difficulty to the framework of general filtration), we obtain…”

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confidence: 85%

Optimal stopping with f-expectations: The irregular case

Grigorova

Imkeller

Ouknine

et al. 2020

Stochastic Processes and their Applications

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We consider the optimal stopping problem with nonlinear f -expectation (induced by a BSDE) without making any regularity assumptions on the payoff process ξ and in the case of a general filtration. We show that the value family can be aggregated by an optional process Y . We characterize the process Y as the E f -Snell envelope of ξ. We also establish an infinitesimal characterization of the value process Y in terms of a Reflected BSDE with ξ as the obstacle. To do this, we first establish some useful properties of irregular RBSDEs, in particular an existence and uniqueness result and a comparison theorem.where T S,T denotes the set of stopping times valued a.s. in [S, T ] and E f S,τ (·) denotes the conditional f -expectation/evaluation at time S when the terminal time is τ .The above non-linear problem has been introduced in [14] in the case of a Brownian filtration and a continuous financial position/pay-off process ξ and applied to the (nonlinear) pricing of American options. It has then attracted considerable interest, in particular, 2 Note that in the case of a not necessarily non-negative pay-off process ξ this result holds up to a translation by the martingale XS := E[ess sup τ ∈T 0,T ξ − τ |FS] (cf. e.g. Appendix A in [30]). More precisely, the property holds forṽ := v + X andξ = ξ + X.

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confidence: 85%

Optimal stopping with f-expectations: The irregular case

Grigorova

Imkeller

Ouknine

et al. 2020

Stochastic Processes and their Applications

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“…For sake of simplicity, a pure OLNED will be simply called an OLNED. Inspired by the literature on optimal stopping in non-zero sum games in discrete time, see among others Grigorova and Quenez (2017); Riedel and Steg (2017), we aim at finding OLNED in the sense of the above definition.…”

Section: Discretised Gamementioning

confidence: 99%

AHEAD : Ad-Hoc Electronic Auction Design

Derchu¹,

Guillot²,

Mastrolia³

et al. 2020

Preprint

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We introduce a new matching design for financial transactions in an electronic market. In this mechanism, called ad-hoc electronic auction design (AHEAD), market participants can trade between themselves at a fixed price and trigger an auction when they are no longer satisfied with this fixed price. In this context, we prove that a Nash equilibrium is obtained between market participants. Furthermore, we are able to assess quantitatively the relevance of ad-hoc auctions and to compare them with periodic auctions and continuous limit order books. We show that from the investors' viewpoint, the microstructure of the asset is usually significantly improved when using AHEAD.

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“…Doubly reflected BSDEs were first introduced and studied by Cvitanić and Karatzas [11] who also showed that classical Dynkin games can be solved using the theory of doubly reflected BSDEs. Their studies were continued by, among others, Bayraktar and Yao [6], Crépey and Matoussi [10], Dumitrescu et al [14], Essaky and Hassani [25], Grigorova et al [27], Grigorova and Quenez [28], Hamadène and Lepeltier [30], Hamadène and Ouknine [31], Hamadène and Wang [32], Kobylanski et al [46], and Lepeltier and San Martín [48]. For a survey of results on Dynkin games and their applications to the valuation and hedging of game options, the reader is referred to Kifer [38].…”

Section: Introductionmentioning

confidence: 95%

Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

Nie,

Rutkowski

2021

Preprint

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We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu [55] and Dumitrescu et al. [13] who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.

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Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs

Cited by 15 publications

References 30 publications

Optimal stopping with f-expectations: The irregular case

Optimal stopping with f-expectations: The irregular case

AHEAD : Ad-Hoc Electronic Auction Design

Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

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