Search results for "programming"
showing 10 items of 3090 documents
Designing and pricing guarantee options in defined contribution pension plans
2015
Abstract The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. However, for DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio and we develop a discrete model that selects the reference portfolio to minimize the cost of a guarantee. While the relation DB–DC is typically viewed as a binary one, the model shows how to price a wide range of guarantees creating a continu…
A dynamical approach to compatible and incompatible questions
2019
We propose a natural strategy to deal with compatible and incompatible binary questions, and with their time evolution. The strategy is based on the simplest, non-commutative, Hilbert space $\mathcal{H}=\mathbb{C}^2$, and on the (commuting or not) operators on it. As in ordinary Quantum Mechanics, the dynamics is driven by a suitable operator, the Hamiltonian of the system. We discuss a rather general situation, and analyse the resulting dynamics if the Hamiltonian is a simple Hermitian matrix.
Quantum jump statistics with a shifted jump operator in a chiral waveguide
2019
Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in the limit of long counting times, which is computed through large deviation theory. We present a wav…
Time-dependent perturbation treatment of independent Raman schemes
2007
The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur.
Partial inner product spaces, metric operators and generalized hermiticity
2013
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP space). Next, we introduce several generalizations of the notion of similarity between operators and explore to what extend they preserve spectral properties. Then we apply some of the previous results to operators on a particular PIP space, namely, a scale of Hilbert spaces generated by a metric operator. Finally, we reformulate the notion of pseudo-hermitian operators in the preceding formalism.
Quadratic ${\mathcal P}{\mathcal T}$-symmetric operators with real spectrum and similarity to self-adjoint operators
2012
It is established that a -symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
2000
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over $\eufrak{h}$. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For $\eufrak{h}=L^2(\mathbb{R}_+)$, the divergence operator is shown to coincide with the Hudson-Parthasarathy quantum stochastic integral for adapted integrable processes and with the non-causal…
Powerful short-cuts for multiple testing procedures with special reference to gatekeeping strategies.
2007
In this paper we present a general testing principle for a class of multiple testing problems based on weighted hypotheses. Under moderate conditions, this principle leads to powerful consonant multiple testing procedures. Furthermore, short-cut versions can be derived, which simplify substantially the implementation and interpretation of the related test procedures. It is shown that many well-known multiple test procedures turn out to be special cases of this general principle. Important examples include gatekeeping procedures, which are often applied in clinical trials when primary and secondary objectives are investigated, and multiple test procedures based on hypotheses which are comple…
Using R via PHP for Teaching Purposes: R-php
2006
This paper deals with the R-php statistical software, that is an environment for statistical analysis, freely accessible and attainable through the World Wide Web, based on R. Indeed, this software uses, as "engine" for statistical analyses, R via PHP and its design has been inspired by a paper of de Leeuw (1997). R-php is based on two modules: a base module and a point-and-click module. R-php base allows the simple editing of R code in a form. R-php point-and-click allows some statistical analyses by means of a graphical user interface (GUI): then, to use this module it is not necessary for the user to know the R environment, but all the allowed analyses can be performed by using the compu…
On surrogating 0–1 knapsack constraints
1999
In this note, we present a scheme for tightening 0–1 knapsack constraints based on other knapsack constraints surrogating.