Stochastic multiresonance

We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic signals may be enhanced at multiple values of the noise level, instead of at a single value which has occurred in systems considered up to now in the framework of stochastic resonance.

Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Coherent stochastic resonance

We consider Brownian motion on a line terminated by two trapping points. A bias term in the form of a telegraph signal is applied to this system. It is shown that the first two moments of survival time exhibit a minimum at the same resonant frequency.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Essays on the treatment of cash flows under stochastic interest rates

Abstract This paper shows how to calculate recursively the moments of the accumulated and discounted value of cash flows when the instantaneous rates of return follow a conditional ARMA process with normally distributed innovations. We investigate various moment based approaches to approximate the distribution of the accumulated value of cash flows and we assess their performance through stochastic Monte-Carlo simulations. We discuss the potential use in insurance and especially in the context of Asset-Liability Management of pension funds.

NUTRIENT DEMAND BY THE CARROT CROP IS INFLUENCED BY THE CULTIVAR

Farmers must carefully choose the cultivar to be grown for a successful carrot crop. The yield potential of the cultivar may influence nutrient demand and should be known to plan for fertilization application. The aim of this study was to evaluate the cultivar effect on carrot yield and on the nutrient content and quantities allocated to leaves and roots. Three experiments were set up in two crop seasons in Rio Paranaíba, MG, Brazil. In the first season, typical summer, 10 summer cultivars were sown. In the second season, summer-winter (transition), two experiments were set up, one with summer cultivars and the other with winter cultivars. The treatments consisted of the carrot cultivars distributed in randomized blocks with four replications. Fresh and dry matter of the roots and leaves was quantified. Yield was calculated based on fresh matter of the roots. The nutrient content in leaves and roots was determined at the time of harvest. These contents and the dry matter production of roots and leaves were used to calculate nutrient uptake and export. The greatest average for total and commercial yield occurred in the crop under summer conditions. Extraction of N and K for most of the cultivars in the three experiments went beyond the amounts applied through fertilizers. Thus, there was contribution of nutrients from the soil to obtain the yields observed. However, the amount of P taken up was considerably less than that applied. This implies that soil P fertility will increase after cropping. The crop season and the cultivars influenced yield, nutrient content in the leaves and roots, and extraction and export of nutrients by the carrot crop.

Stochastic resonance in a suspension of magnetic dipoles under shear flow

We show that a magnetic dipole in a shear flow under the action of an oscillating magnetic field displays stochastic resonance in the linear response regime. To this end, we compute the classical quantifiers of stochastic resonance, i.e., the signal to noise ratio, the escape time distribution, and the mean first passage time. We also discuss the limitations and role of the linear response theory in its applications to the theory of stochastic resonance.

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seiferts integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Stochastic resonance in nonpotential systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.

Stochastic resonance in a system of magnetic particles

We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the distribution of residence times, and the mean first passage time. The behavior of these quantities is similar to the behavior of corresponding quantities in other systems where stochastic resonance has also been observed.

Less Risk, More Effort : Demand Risk Allocation in Incomplete Contracts

This article investigates the allocation of demand risk within an incomplete contract framework. We consider an incomplete contractual relationship between a public authority and a private provider (i.e. a public-private partnership), in which the latter invests in non-verifiable cost-reducing efforts and the former invests in non-verifiable adaptation efforts to respond to changing consumer demand over time. We show that the party that bears the demand risk has fewer hold-up opportunities and that this leads the other contracting party to make more effort. Thus, in our model, bearing less risk can lead to more effort, which we describe as a new example of âeuro~counter-incentivesâeuro?. We further show that when the benefits of adaptation are important, it is socially preferable to design a contract in which the demand risk remains with the private provider, whereas when the benefits of cost-reducing efforts are important, it is socially preferable to place the demand risk on the public authority. We then apply these results to explain two well-known case studies.

European guidelines for the development of mechanisms/tools supporting the individual demand for training through use of training Vouchers

El projecte de TAV es basa en la transferència d'un sistema de vals de capacitació, i en com aquest sistema de vals és adaptable a altres països o regions. En el document s'analitzen diferents conceptes teòrics sobre la conveniència o no de la implantació d'aquest sistema. A més a més, aquest document és una guia per a les organitzacions interessades en l'adaptació del sistema de vals formatius al seu territori, mostrant els passos a seguir i oferint eines útils per aconseguir-ho.