A THEORETICAL FRAMEWORK FOR THE PRICING OF CONTINGENT CLAIMS IN THE PRESENCE OF MODEL UNCERTAINTY

By Laurent Denis, Claude Martini. 2006

371 citations recorded by the source corpus.

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda, Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. We obtain a partial characterization result and a full characterization which extends Avellaneda, Levy and Paras results in the UVM case.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/ba5ff6431ff4dbb370ead4aa78cc36f7f0563564

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Citations in the corpus

Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation (2006, methodology): “During the reversion process of this paper, the author has found a very interesting paper [ 18 ] by Denis and Martini on super-pricing of contingent claims under model uncertainty of volatility.”
A New Central Limit Theorem under Sublinear Expectations (2008, background): “3 Just as in the framework of a probability space, a sublinear expectation space can be a completed Banach space under its natural norm ‖·‖ =Ê[|·|] (see [11]-[16]) and by using its natural capacity ĉ(·) induced via Ê[|·|] (see [4] and [3]).”
Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems (2013, background): “stochastic diﬀerential equations (see e.g. Stroock and Varadhan [33]) as well as control problems [13] etc. Moreover, a renewed interest in canonical formulation comes from works of Denis and Martini [11] on G-expectation as well as Soner, Touzi and Zhang [30] on second order BSDEs. In the control p”
Superreplication under Volatility Uncertainty for Measurable Claims (2012, methodology): “A. Neufeld gratefully acknowledges financial support by Swiss National Science Foundation Grant PDFMP2-137147/1.”
The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, background): “The case of arbitrary measures which satisfy (2.4) for n = 2 was solved in Brown, Hobson and Rogers [9].”
ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL (2015, background): “However, as shown in Denis and Martini (2006) for instance, our smaller set PH is only relatively compact for the weak topology.”
Martingale optimal transport and robust hedging in continuous time (2012, background): “] assumes a large class of possible martingale measures for the price process. The duality is then proved by extending an earlier unconstrained result proved in [35]. As in the unconstrained model of [13, 35, 36], the super replication is deﬁned not path-wise but rather probabilistically through qua”
Optimal Stopping under Nonlinear Expectation (2012, background): “[4] Denis, L. and Martini, C. (2006) A Theorectical Framework for the Pricing of Contingent Claims in the Presence of Model Uncertainty, Annals of Applied Probability, 16 (2), 827-852.”
On the Robust superhedging of measurable claims (2013, positive): “Motivated by the original works of Avellaneda [1] and Lyons [2], the first general formulation of this problem was introduced by Denis and Martini [4] by considering the hedging problem under a nondominated family of probability measures on the canonical space of continuous trajectories.”
Stopping times and related Itô's calculus with G-Brownian motion (2009, background): “The space L(2)G(Ω) was also intruduced independently in [3] in a quite different framework.”
Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications (2014, methodology): “Denis and Martini (2006), Gilboa (1987), Marinacci (1999), Peng (1997, 1999, 2006, 2008a) etc.”
Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm (2014, methodology): “Non-additive probabilities and non-additive expectations are useful tools for studying uncertainties in statistics, measures of risk, superhedging in finance and non-linear stochastic calculus, c.f. Denis and Martini (2006), Gilboa (1987), Marinacci (1999), Peng (1997, 1999, 2006, 2008a) etc.”
Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, neutral): “Email:stazlx@zju.edu.cn 1 stochastic calculus, cf. Denis and Martini (2006), Gilboa (1987), Marinacci (1999), Peng (1999, 2006, 2008a) etc.”
Random G-expectations. (2010, background): “See also Denis and Martini [5] for a general study of related capacities.”
Backward stochastic differential equations driven by G-Brownian motion (2012, background): “Thus, we need a new coherent framework on which one can accommodate problems involving a family of nondominated measures (see [4]).”