Dynamic programming for stochastic target problems and geometric flows

By G. Flows, H. M. Soner, Nizar Touzi. 2002

170 citations recorded by the source corpus.

Subfields: Applied Mathematics, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/643c94c7d9ed852f74d40521e197686bd4e73313

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Citations in the corpus

A stochastic representation for mean curvature type geometric flows (2003, methodology): “Indeed under some assumptions, the authors in [24] proved that”
Superreplication under Volatility Uncertainty for Measurable Claims (2012, methodology): “This is simple when there are only countably many values; therefore, following a construction of [20], we use an approximation argument.”
Quasi-sure Stochastic Analysis through Aggregation (2010, unknown): “page 5 in [14].”
Zero-sum stochastic differential games of generalized McKean–Vlasov type (2018, background): “5 in [25]) the space (At, ρKr) is separable since the σ-algebra F t T⊗B([0, T ]) is countably generated up to null sets.”
A stochastic target formulation for optimal switching problems in finite horizon (2009, methodology): “Following [2] and [16], we rely on the direct dynamic programming principle of [17].”
Option pricing with linear market impact and nonlinear Black–Scholes equations (2018, unknown): “The two problems are not equivalent in all cases, in particular when the exact replication equation is not parabolic (see [1, 33]).”
The multi-dimensional super-replication problem under gamma constraints (2005, methodology): “In this paper, we continue with the method develo Soner and Touzi in [15], and later in [16] and [17], in order to derive the DPE for (1.”
Conditional Essential Suprema with Applications (2003, background): “Consider the special case considered by Soner and Touzi [14], [15] and Buckdahn et al.”
McKean–Vlasov optimal control: The dynamic programming principle (2019, result): “They establish a general geometric dynamic programming, thus extending the seminal results of Soner and Touzi [76] corresponding to the non–McKean–Vlasov case.”
A Geometrical Approach to the Study¶of Unbounded Solutions¶of Quasilinear Parabolic Equations (2002, background): “3) (and even more general geometrical equations) have been established independently by Soner & Touzi [33,34] and by Buckdahn, Cardaliaguet & Quincampoix [12].”
A deterministic‐control‐based approach to fully nonlinear parabolic and elliptic equations (2010, background): “In brief: the present paper is to [12] as our prior paper [28] was to [8, 34].”