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

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

Assessment of human influenza pandemic scenarios in Europe

The response to the emergence of the 2009 influenza A(H1N1) pandemic was the result of a decade of pandemic planning, largely centred on the threat of an avian influenza A(H5N1) pandemic. Based on a literature review, this study aims to define a set of new pandemic scenarios that could be used in case of a future influenza pandemic. A total of 338 documents were identified using a searching strategy based on seven combinations of keywords. Eighty-three of these documents provided useful information on the 13 virus-related and health-system-related parameters initially considered for describing scenarios. Among these, four parameters were finally selected (clinical attack rate, case fatality rate, hospital admission rate, and intensive care admission rate) and four different levels of severity for each of them were set. The definition of six most likely scenarios results from the combination of four different levels of severity of the four final parameters (256 possible scenarios). Although it has some limitations, this approach allows for more flexible scenarios and hence it is far from the classic scenarios structure used for pandemic plans until 2009

Invariant and polynomial identities for higher rank matrices

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from

Algebraic invariants of five qubits

The Hilbert series of the algebra of polynomial invariants of pure states of five qubits is obtained, and the simplest invariants are computed.Comment: 4 pages, revtex. Short discussion of quant-ph/0506073 include