3,919 research outputs found
Quadratic BSDEs with convex generators and unbounded terminal conditions
In a previous work, we proved an existence result for BSDEs with quadratic
generators with respect to the variable z and with unbounded terminal
conditions. However, no uniqueness result was stated in that work. The main
goal of this paper is to fill this gap. In order to obtain a comparison theorem
for this kind of BSDEs, we assume that the generator is convex with respect to
the variable z. Under this assumption of convexity, we are also able to prove a
stability result in the spirit of the a priori estimates stated in the article
of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can
derive the nonlinear Feynman--Kac formula in this context
Nilpotent polynomials approach to four-qubit entanglement
We apply the general formalism of nilpotent polynomials [Mandilara et al,
Phys. Rev. A 74, 022331 (2006)] to the problem of pure-state multipartite
entanglement classification in four qubits. In addition to establishing contact
with existing results, we explicitly show how the nilpotent formalism naturally
suggests constructions of entanglement measures invariant under the required
unitary or invertible class of local operations. A candidate measure of
fourpartite entanglement is also suggested, and its behavior numerically tested
on random pure states.Comment: 11 pages, 1 figure. Finalised versio
Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem
In this paper, we study a class of quadratic Backward Stochastic Differential
Equations (BSDEs) which arises naturally when studying the problem of utility
maximization with portfolio constraints. We first establish existence and
uniqueness results for such BSDEs and then, we give an application to the
utility maximization problem. Three cases of utility functions will be
discussed: the exponential, power and logarithmic ones
Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian
We consider Hamilton Jacobi Bellman equations in an inifinite dimensional
Hilbert space, with quadratic (respectively superquadratic) hamiltonian and
with continuous (respectively lipschitz continuous) final conditions. This
allows to study stochastic optimal control problems for suitable controlled
Ornstein Uhlenbeck process with unbounded control processes
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