1,025 research outputs found
Stochastic integrals and conditional full support
We present conditions that imply the conditional full support (CFS) property,
introduced by Guasoni, R\'asonyi, and Schachermayer [Ann. Appl. Probab., 18
(2008), pp. 491--520], for processes Z := H + K \cdot W, where W is a Brownian
motion, H is a continuous process, and processes H and K are either progressive
or independent of W. Moreover, in the latter case under an additional
assumption that K is of finite variation, we present conditions under which Z
has CFS also when W is replaced with a general continuous process with CFS. As
applications of these results, we show that several stochastic volatility
models and the solutions of certain stochastic differential equations have CFS.Comment: 19 pages, v3: almost entirely rewritten, new result
Constructing Sublinear Expectations on Path Space
We provide a general construction of time-consistent sublinear expectations
on the space of continuous paths. It yields the existence of the conditional
G-expectation of a Borel-measurable (rather than quasi-continuous) random
variable, a generalization of the random G-expectation, and an optional
sampling theorem that holds without exceptional set. Our results also shed
light on the inherent limitations to constructing sublinear expectations
through aggregation.Comment: 28 pages; forthcoming in 'Stochastic Processes and their
Applications
GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization
In this paper we provide Galtchouk-Kunita-Watanabe representation results in
the case where there are restrictions on the available information. This allows
to prove existence and uniqueness for linear backward stochastic differential
equations driven by a general c\`adl\`ag martingale under partial information.
Furthermore, we discuss an application to risk-minimization where we extend the
results of F\"ollmer and Sondermann (1986) to the partial information framework
and we show how our result fits in the approach of Schweizer (1994).Comment: 22 page
Utility maximization with random horizon: a BSDE approach
International audienceIn this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations
Coupling strategies for compressible - low Mach number flows
International audienceIn order to enrich the modelling of fluid flows, we investigate in this paper a coupling between two models dedicated to distinct regimes. More precisely, we focus on the influence of the Mach number as the low Mach case is known to induce theoretical and numerical issues in a compressible framework. A moving interface is introduced to separate a compressible model (Euler with source term) and its low Mach counterpart through relevant transmission conditions. A global steady state for the coupled problem is exhibited. Numerical simulations are then performed to highlight the influence of the coupling by means of a robust numerical strategy
Axiomatizations of Lov\'asz extensions of pseudo-Boolean functions
Three important properties in aggregation theory are investigated, namely
horizontal min-additivity, horizontal max-additivity, and comonotonic
additivity, which are defined by certain relaxations of the Cauchy functional
equation in several variables. We show that these properties are equivalent and
we completely describe the functions characterized by them. By adding some
regularity conditions, these functions coincide with the Lov\'asz extensions
vanishing at the origin, which subsume the discrete Choquet integrals. We also
propose a simultaneous generalization of horizontal min-additivity and
horizontal max-additivity, called horizontal median-additivity, and we describe
the corresponding function class. Additional conditions then reduce this class
to that of symmetric Lov\'asz extensions, which includes the discrete symmetric
Choquet integrals
Projections, Pseudo-Stopping Times and the Immersion Property
Given two filtrations , we study under which
conditions the -optional projection and the -dual
optional projection coincide for the class of -optional processes
with integrable variation. It turns out that this property is equivalent to the
immersion property for and , that is every -local martingale is a -local martingale, which, equivalently, may
be characterised using the class of -pseudo-stopping times. We also
show that every -stopping time can be decomposed into the minimum of
two barrier hitting times
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