Model-free superhedging duality

Burzoni, Matteo; Frittelli, Marco; Maggis, Marco

doi:10.1214/16-aap1235

Cited by 55 publications

(74 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the last assertion, suppose Ω is analytic. From Remark 5.6 in Burzoni et al (2017), Ω * is also analytic. In particular, if M Ω = ∅ then, from Corollary 3.3, Q(Ω * ) = 1 for any Q ∈ M Ω .…”

Section: Classical Model Specific Setting and Its Selection Of Scenariosmentioning

confidence: 84%

“…The remaining of Step 1,Step 2,Step 3,Step 4 and Step 5 follows replicating the argument in Burzoni et al (2017).…”

Section: Proof Of the Ftap And Pricing Hedging Duality When No Optionmentioning

confidence: 99%

“…Following the intuition in Burzoni et al (2017), we expect to obtain pricing-hedging duality only when considering superhedging on the set of scenarios visited by martingales, i.e. we consider π Ω * Φ ,Φ (g).…”

Section: Fundamental Theorem Of Asset Pricing and Superhedging Dualitymentioning

confidence: 99%

See 2 more Smart Citations

Pointwise Arbitrage Pricing Theory in Discrete Time

et al. 2019

Self Cite

View full text Add to dashboard Cite

We develop a robust framework for pricing and hedging of derivative securities in discretetime financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain an abstract (pointwise) Fundamental Theorem of Asset Pricing and Pricing-Hedging Duality. Our results are general and in particular include so-called model independent results of Acciaio et al. (2016); Burzoni et al. (2016) as well as seminal results of Dalang et al. (1990) in a classical probabilistic approach.Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure. In this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.

show abstract

Section: Classical Model Specific Setting and Its Selection Of Scenariosmentioning

confidence: 84%

“…The remaining of Step 1,Step 2,Step 3,Step 4 and Step 5 follows replicating the argument in Burzoni et al (2017).…”

Section: Proof Of the Ftap And Pricing Hedging Duality When No Optionmentioning

confidence: 99%

See 1 more Smart Citation

Pointwise Arbitrage Pricing Theory in Discrete Time

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…In continuous time models under volatility uncertainty, analogous pricing-hedging duality results have been obtained by, among many others, Denis and Martini (2006), Soner, Touzi, and Zhang (2013), Neufeld and Nutz (2013), and Possamaï, Royer, and Touzi (2013). In discrete time, a general pricing-hedging duality was shown in, for example, Bouchard and Nutz (2015) and Burzoni, Frittelli, and Maggis (2017). Importantly, in a robust setting, one often wants to include additional market instruments, which may be available for trading.…”

Section: Introductionmentioning

confidence: 99%

The robust pricing–hedging duality for American options in discrete time financial markets

Aksamit

Deng

Obłój

et al. 2018

Mathematical Finance

View full text Add to dashboard Cite

We investigate the pricing–hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, for example, a family of European options, only statically. In the first part of the paper, we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a nondominated family of probability measures. Our first insight is that, by considering an enlargement of the space, we can see American options as European options and recover the pricing–hedging duality, which may fail in the original formulation. This can be seen as a weak formulation of the original problem. Our second insight is that a duality gap arises from the lack of dynamic consistency, and hence that a different enlargement, which reintroduces dynamic consistency is sufficient to recover the pricing–hedging duality: It is enough to consider fictitious extensions of the market in which all the assets are traded dynamically. In the second part of the paper, we study two important examples of the robust framework: the setup of Bouchard and Nutz and the martingale optimal transport setup of Beiglböck, Henry‐Labordère, and Penkner, and show that our general results apply in both cases and enable us to obtain the pricing–hedging duality for American options.

show abstract

“…This follows from the result proven in Dolinsky & Neufeld (2018) that for fully incomplete markets, the set of all equivalent local martingale measures are weakly dense in the set of all local martingale measures defined on the continuous path space. For more papers related to robust pricing, in particular to duality results, we refer to Acciaio et al (2016); Bartl et al (2018Bartl et al ( , 2017; Burzoni et al (2017); Dolinsky & Soner (2014, 2015; Guo et al (2017); Hobson (1998) ;Hou & Obłój (2018) to name but a few.…”

Section: Introductionmentioning

confidence: 99%

Buy-and-Hold Property for Fully Incomplete Markets When Super-Replicating Markovian Claims

Neufeld

2018

Int. J. Theor. Appl. Finan.

View full text Add to dashboard Cite

We show that when the price process S represents a fully incomplete market, the optimal super-replication of any Markovian claim g(S T ) with g(·) being nonnegative and lower semicontinuous is of buy-and-hold type. Since both (unbounded) stochastic volatility models and rough volatility models are examples of fully incomplete markets, one can interpret the buy-and-hold property when super-replicating Markovian claims as a natural phenomenon in incomplete markets.

show abstract

Model-free superhedging duality

Cited by 55 publications

References 21 publications

Pointwise Arbitrage Pricing Theory in Discrete Time

Pointwise Arbitrage Pricing Theory in Discrete Time

The robust pricing–hedging duality for American options in discrete time financial markets

Buy-and-Hold Property for Fully Incomplete Markets When Super-Replicating Markovian Claims

Contact Info

Product

Resources

About