Stochastic Analysis and Mathematical Physics VI
Jan 3-9 2008, Facultad de Matemáticas, PUC, Chile.
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Investment Timing in Presence of Downside Risk: A Certainty Equivalent Characterization 
Luis H. R. Alvarez
Turku School of Economics
(joint research with my PhD-student Teppo Rakkolainen)
Abstract: We demonstrate that the value of a single threshold investment strategy under stochastic dynamics allowing both continuous fluctuations and instantaneous downward jumps has a certainty equivalent representation in terms of the value of this strategy under risk-adjusted deterministic dynamics, and that this risk adjustment can be made either to the discount rate or to the expected infinitesimal growth rate of the underlying. In this way our analysis characterizes a class of optimal timing problems of irreversible investments for which the solution of the stochastic problem coincides with the solutions of certain risk-adjusted deterministic optimal timing problems.


Date received: November 6, 2007

 


On the dynamics of a Hall system driven by a time dependent magnetic flux line
Joachim Asch
CPT Marseille and USTV, France

Abstract: We present aspects of the dynamics of particles moving in a punctured plane under the influence of a homogeneous magnetic field, an electric background, and driven by a time-dependent singular flux tube through the hole. 

Date received: October 31, 2007




Repeated quantum interactions and random walks on U(n)
Stephane Attal
Université Lyon I

Abstract: The physical model of a quantum system undergoing repeated quantum interactions with an environment constituted of a chain of identical systems gives rises to a quantum dynamics which is at the same time Hamiltonian and Markovian. We explore the case when such dynamics are driven by classical noises. A deep algebraic structure emerges, connected to the notion of "obtuse random walks".

Date received: November 6, 2007





The Quantum Fokker-Planck semigroup
Franco Fagnola
Politécnico di Milano

Abstract: We discuss the qualitative behaviour of a quantum Markov semigroup arising in the study of nanoscale semiconductor devices: the linear part of the so-called quantum Fokker-Planck semigroup. We illustrate methods based on non-commutative versions of Liapounov functions for proving the existence (or absence) of invariant states and the study of irreducibility allowing us to determine their support projection and eventually establish uniqueness.
Reference:
F. Fagnola and R.Rebolledo, Notes on the qualitative behaviour of quantum Markov semigroups.
In: S.Attal, A.Joye, C.-A. Pillet (eds.) Open Quantum Systems III. LNM
1882, 161--205, (2006).

Date received: November 14, 2007


Bernoulli decomposition of random variables and applications
François Germinet
Université de Cergy-Pontoise
Abstract: We introduce a general decomposition of real random variables in terms of a Bernoulli part. We provide applications of this Bernoulli decomposition in several domains such as combinatorics (Sperner theory), singularity of random matrices, anti-concentration bounds for functions of random variables. The main application is a proof of Anderson localization for random Schroedinger operators with arbitrary single site probability measure.

Date received: December 25, 2007




Martingale optimality ans cross hedging of insurance derivatives 
Peter Imkeller
Humboldt University at Berlin

Abstract: A financial market model is considered on which agents (e.g. insurers) are subject to an exogenous financial risk, which they trade by issuing a risk bond. Typical risk sources are climate or weather. Buyers of the bond are able to invest in a market asset correlated with the exogenous risk. We investigate their utility maximization problem with respect to the correlation, and calculate bond prices using utility indifference. Prices are seen to decrease as a result of dynamic hedging. Theincrements are interpreted in terms of diversification pressure.

Date received: September 26, 2007



Repeated Interaction Quantum Systems: Deterministic and Random
Alain Joye

Institut Fourier, Universite de Grenoble

Abstract: Consider a quantum system of reference interacting in sequence with the successive elements of an infinite chain of quantum sub-systems. When the elements of the chain and the interactions between these elements and the reference system are identical, we speak of deterministic repeated interaction quantum systems. We will also consider cases where the elements of the chain and/or the successive interactions with the reference system are random. We consider the dynamics of certain observables, in particular those acting on the reference system only. We show that the states on these observables almost surely converge asymptotically in time to a deterministic state, the properties of which will be discussed.
This is joint work with L.Bruneau and M.Merkli.

Date received: : November 5, 2007

 


Strong solutions to stochastic Volterra equations of convolution type
Anna Karczewska
University of Zielona Góra, Poland


Abstract


Date received: October 25, 2007




Generation of cosine families on Lp(0,1) by elliptic operators with Robin boundary conditions

Valentin Keyantuo

University of Puerto Rico


Abstract

Date received: December 20, 2007



Stability Radii
Wolfgang Kliemann
Pontificia Unniversidad Católica de Chile

Abstract

Date received: November 23, 2007




Lifshitz tails for non monotonous alloy type models
Frédéric Klopp

Université de Paris 13

Abstract: For a standard alloy or Anderson type random perturbations of the free Laplace operator, it is well known that Lifshitz tails occur at the bottom of the spectrum when the single site potential is sign definite. In this work, we shall present some results in the case when the single site potential is not sign definite. The talk is based on joint work with S. Nakamura (Univ. Tokyo).

Date received: December 21, 2007



Occupation fields and Gaussian fields
Yves Le Jan

Université Paris-Sud


Abstract: The relation between Gaussian free fields and occupation fields of Markov processes is revisited.

Date received: November 6, 2007





The method of the weakly conjugate operator

Marius Mantoiu

Universidad de Chile


Abstract: We present a commutator method to prove boundary estimates on the resolvent and the absence of singular spectrum for selfadjoint operators. It is an extension to unbounded operators of the Kato-Putnam Theorem and it is related to Mourre theory. We illustrate it with applications to generalized Schroedinger and Dirac operators and to operators acting on graphs and on locally compact groups.

Date received: November 15, 2007




Simultaneous Exact Control for the Maxwell equations and a vector wave equation
Gustavo Perla Menzala

National laboratory of scientific computation, Brazil

Abstract: In this talk we describe new results we obtain recently on the subject using the multiplier technique together with new identities associated to both systems. This allow us to obtain a boundary observation inequality in order to applied the Hilbert Uniqueness Method due to J.L.Lions. The method seems to extend to treat anisotropic Maxwell equations. This a joint work with B.Kapitonov.

Date received: October 8, 2007




The two-photon absorption and emission process
Roberto Quezada

Universidad Autonoma Metropolitana, Iztapalapa Campus, Mexico City


Abstract: We shall discuss some important properties of the quantum Markov semigroup of the two-photon absorption and emission process, including the existence of equilibrium states, the convergence to equilibrium as well as the computation of the rate of convergence to the equilibrium.

Date received: November 14, 2007

 
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