Oriented Distance Functions in Shape Analysis and Optimization

Delfour, Michel C.; Zolésio, Jean-Paul

doi:10.1007/978-1-4613-8460-1_3

Cited by 7 publications

(2 citation statements)

References 11 publications

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“…Let (Y, Z) be the unique solution of BSDE (8). Then, the value function V (0, x) of the optimization problem (3) with admissible set A and the associated optimal trading strategy π * ∈ A are given, respectively, as in (10) and (11).…”

Section: Definition 9 [Admissible Strategies With Constraints 3]mentioning

confidence: 99%

Exponential utility maximization and indifference valuation with unbounded payoffs

Hu¹,

Liang²,

Tang³

2017

Preprint

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We solve an exponential utility maximization problem with unbounded payoffs under general portfolio constraints, via the theory of quadratic backward stochastic differential equations with unbounded terminal data. This generalizes the previous work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691-1712 from the bounded to an unbounded framework. Furthermore, we study utility indifference valuation of financial derivatives with unbounded payoffs, and derive a novel convex dual representation of the prices. In particular, we obtain new asymptotic behavior as the risk aversion parameter tends to either zero or infinity.

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Section: Definition 9 [Admissible Strategies With Constraints 3]mentioning

confidence: 99%

Exponential utility maximization and indifference valuation with unbounded payoffs

Hu¹,

Liang²,

Tang³

2017

Preprint

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“…Generally, the parameterization of the level set function Φ is done by the oriented distance function denoted b Ω t , see [2,3] for references:…”

Section: Shape Identification Using a Galerkin-level Set Strategymentioning

confidence: 99%

Galerkin Strategy for Level Set Shape Analysis: Application to Geodesic Tube

Blanchard

Zolésio

2009

IFIP Advances in Information and Communication Technology

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Abstract. In this paper, we consider the geodesic tube characterization using a Galerkin-Level Set strategy. The first section is devoted to the analysis of a geodesic tube construction between two sets through the definition of the shape metric. In the second section, we define the Galerkin-Level Set strategy in shape analysis. This new variational formulation associated to a Hilbert space metric for shape identification problem consists in parameterizing the level set function in a finite dimensional subspace spanned by linear independent functions. Consequently, this method is more focused on topological changes than on high accuracy for the boundary evaluation as in a traditional level set formulation. In the third section, we use the Galerkin-Level Set formulation applied to a geodesic tube construction between two sets, through the calculus of the shape derivative of the normal speed. Finally, this geodesic tube construction is validated by a numerical experiment. Tube Formulation Using Moving DomainIn this section, we briefly recall the concept of connecting tube, introduced in [6]. Let us consider D as a bounded universe in R n and two open sets domains Ω 0 , Ω 1 ⊂ D. We denote the initial domain by Ω 0 and the final domain by Ω 1 , and consider the tube connecting Ω 0 with Ω 1 defined by the n + 1 dimensional graph of an n-dimensional moving domain: see Fig. 1. Consequently, considering the time interval I = [0, 1], we define the tube evolution Q by product space, using the cylinder I × Ω as follows:Moreover, we denote by Σ the lateral boundary of the tube, defined by the following expression: Σ = 0≤t≤1 {t} ×Γ t , where Γ t denotes the boundary of Ω t . The characteristic function of the tube is defined by ζ (t, x) de f = χ Ω t (x) and verifies ζ 2 = ζ . Following [4,5], the set of connecting tubes between Ω 0 and Ω 1 is defined by:

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