Duality and convergence for binomial markets with friction

Dolinsky, Yan; Soner, H. Meté

doi:10.1007/s00780-012-0192-1

Cited by 34 publications

(66 citation statements)

References 26 publications

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“…At last, the Theorem 3.1 in (Dolinsky & Soner, 2013) is recalled in the following remark. It claims that a dual of the super-replication price is an optimal control problem in which the controller is allowed to choose any probability measure on (Ω n , F (n)) in their binomial model.…”

Section: Super-replication Problemmentioning

confidence: 99%

“…The proof idea for the lower bound part of Theorem 3.5 in (Dolinsky & Soner, 2013) is used in the following proof of Theorem 1.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…And, the proof given in it was limited to Markovian claims. (Dolinsky & Soner, 2013) took the one-dimensional binomial version of model proposed by (Cetin, Jarrow & Protter, 2004), which was also adopted in (Cetin & Roger, 2007) and (Gokay & Soner, 2012). Their paper was based on nonmarkovian claims and more general liquidity functions, which was an extension of (Gokay & Soner, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Their paper was based on nonmarkovian claims and more general liquidity functions, which was an extension of (Gokay & Soner, 2012). In (Dolinsky & Soner, 2013), the dual of the discrete model was derived as an optimal control problem and the construction given in (Kusuoka, 1995) was applied to prove that a liquidity premium exists.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Liquidity Premiums in a Levy Market

Mei¹

2015

JMR

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This paper gives a theorem for the continuous time super-replication cost of European options where the stock price follows an exponential Lévy process. Under a mild assumption on the legend transform of the trading cost function, the limit of the sequence of the discrete super-replication cost is proved to be greater than or equal to an optimal control problem. The main tool is an approximation multinomial scheme based on a discrete grid on a finite time interval [0,1] for a pure jump Lévy model. This multinomial model is constructed similar to that proposed by (Szimayer & Maller, Stoch. Proce. & Their Appl., 117, 1422-1447. Furthermore, it is proved that the existence of a liquidity premium for the continuous-time model under a Lévy process. This paper concentrates on the Lévy processes with infinitely many jumps in any finite time interval. The approach overcomes some difficulties that can be encountered when the Lévy process has infinite activity.

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Section: Super-replication Problemmentioning

confidence: 99%

“…The proof idea for the lower bound part of Theorem 3.5 in (Dolinsky & Soner, 2013) is used in the following proof of Theorem 1.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Liquidity Premiums in a Levy Market

Mei¹

2015

JMR

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“…Super-replication cost or related problems were studied in (Cetin, Soner & Touzi, 2010), (Gokay & Soner, 2012), (Dolinsky & Soner, 2012) and (Xing, 2015). In (Cetin, Soner & Touzi, 2010), the existence of the continuous time super-replication cost from a binomial model was shown.…”

Section: Introductionmentioning

confidence: 99%

Existence Conditions of Super-Replication Cost in a Multinomial Model

Mei¹

2017

JMR

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This paper gives a theorem for the continuous time super-replication cost of European options in an unbounded multinomial market. An approximation multinomial scheme is put forward on a finite time interval [0,1] corresponding to a pure jump Lévy model with unbounded jumps. Under the assumption that the expected underlying stock price at time 1 is bounded, the limit of the sequence of the super-replication cost in a multinomial model is proved to be greater than or equal to an optimal control problem. Furthermore, it is discussed that the existence conditions of a super-replication cost and a liquidity premium for the multinomial model. This paper concentrates on a multinomial tree with unbounded jumps, which can be seen as an extension of the work of (Xing, 2015). The super-replication cost and the liquidity premium under the variance gamma model and the normal inverse Gaussian model are calculated and illustrated.

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Martingale optimal transport and robust hedging in continuous time

Dolinsky

Soner

2013

Probab. Theory Relat. Fields

Self Cite

213

258

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The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

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Duality and convergence for binomial markets with friction

Cited by 34 publications

References 26 publications

Liquidity Premiums in a Levy Market

Liquidity Premiums in a Levy Market

Existence Conditions of Super-Replication Cost in a Multinomial Model

Martingale optimal transport and robust hedging in continuous time

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