ROBUST BOUNDS FOR FORWARD START OPTIONS

By David Hobson *, Anthony Neuberger. 2012

147 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/0cff819a509a16a4556294c42af3dd551e77e1d9

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Citations in the corpus

The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, background): “It also discusses the link with martingale optimal transport.”
Complete Duality for Martingale Optimal Transport on the Line (2015, background): “On the other hand, [26, 27] find the optimal transports for f(x, y) = ±|x − y|.”
Martingale optimal transport and robust hedging in continuous time (2012, result): “olio of an investor consists of static positions in the call options in addition to the usual dynamically updated risky asset. This leads us to a similar structure to that in [19] and in other papers [6, 8, 10, 11, 14, 15, 18, 21, 22, 23, 24, 25, 29] which consider modelindependent pricing. This app”
Martingale Benamou–Brenier: A probabilistic perspective (2017, background): “Early papers to investigate such problems include [33, 11, 53, 23, 22, 20], and this topic is commonly referred to as martingale optimal transport.”
A new class of costs for optimal transport planning (2018, background): “This problem was introduced in the one-dimensional case X , Y ⊂R in [12] for the special cost c(x, y)=− |x− y| and for more general costs in [4] in the context of mathematical finance, to obtain robust modelindependent bounds on option prices: in both works the authors obtain existence for the prima”
Irreducible convex paving for decomposition of multidimensional martingale transport plans (2017, methodology): “The robust superhedging problem was introduced by Hobson [14], and was addressing specific examples of exotic derivatives by means of corresponding solutions of the Skorohod embedding problem, see [6, 15, 16], and the survey [14].”
Optimal transport and Skorokhod embedding (2013, background): “The first papers to study such problems include [7,19,23,32], and this field is commonly referred to as martingale optimal transport.”
Martingale optimal transport in the Skorokhod space (2014, result): “The structure studied in this paper is similar to that of [19] and also of [6, 9, 10, 11, 13, 14, 15, 18, 21, 22, 23, 24, 25, 27].”
Stability of martingale optimal transport and weak optimal transport (2019, unknown): “tter class of problems from this viewpoint. 1.1. Stability of martingale optimal transport. The martingale optimal transport problem is a variant of (OT) stemming from robust mathematical ﬁnance (cf. [29, 14, 38, 21, 20, 17, 12, 8, 31, 32, 35, 19, 30, 22, 27] among many others). In order to deﬁne th”
Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems (2017, unknown): “The optimality of π? for % = 1 was obtained by [11] in Example 6.”
On a problem of optimal transport under marginal martingale constraints (2012, background): “The Hobson–Neuberger cost function and its converse.”
Structure of optimal martingale transport plans in general dimensions (2015, methodology): “(Beiglböck-Juillet [5], Hobson-Neuberger [22], Hobson-Klimmek [21]) Assume that μ and ν are probability measures in convex order on R, and that μ is continuous.”
All adapted topologies are equal (2019, unknown): “[34, 13, 27, 23, 17, 33, 18, 12, 14] among many others).”
Model-independent bounds for option prices—a mass transport approach (2011, unknown): “Our counterexample fits into the framework11 of [26], i.”
Adapted Wasserstein distances and stability in mathematical finance (2019, methodology): “Recently this has been complemented by techniques coming from (martingale) optimal transport, early papers which advance this viewpoint include [38, 15, 29, 16, 21, 26, 24, 18].”
An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, unknown): “…constraints, see e.g. Brown, Hobson & Rogers [13], Madan & Yor [62], Cox, Hobson & Oblój [18], Cox & Oblój [19] [20], Davis, Oblój & Raval [23], Cox & Wang [22], Gassiat, Oberhauser & dos Reis [34], Cox, Oblój & Touzi [21], Hobson & Neuberger [51], and Hobson & Klimmek [47] [48] [49] [50].”
The Wasserstein space of stochastic processes (2021, background): “The counterpart of this result for European option has been known for some time and lies at the basis of the fruitful interaction of robust finance and (martingale) optimal transport in the last decade, see [41, 33, 40, 29, 22, 19, 37, 26] among many others.”