Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

"Vegeu el resum a l'inici del document del fitxer adjunt."

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

El Procés de la certificació energètica per edificació existent

Arran d’una part de la transposició a l’Estat espanyol de la Directiva 2002/91/CE sobre Eficiència Energètica d’Edificis mitjançant el Real Decret 47/2007, pel que s’aprova el Procediment bàsic per la certificació d’eficiència energètica d’edificis de nova construcció, la certificació energètica esdevé obligatòria per edificació nova, i es dóna de termini fins a 2009 per a l’obligatorietat en edificació existent. És en aquest buit de l’edificació existent on es presenta l’objectiu de l’estudi, que és precisament augmentar el coneixement i canvi d’actitud dels agents de l’habitatge social sobre solucions de la rehabilitació des d’una perspectiva de sostenibilitat ambiental, en el context de la certificació energètica per obra nova. Després d’un intens treball de recerca de dades, s’aplicà en un cas pràctic d’habitatge social la nova directiva sobre certificació energètica de l’edificació amb les eines oficials existents. S’aconseguí fer una avaluació energètica d’un habitatge com a eina de gestió per la definició d’estratègies, i solucions ambientals per aconseguir així una major eficiència dels mateixos. D’aquesta manera, s’ha demostrat el valor afegit de la certificació energètica, i les dades obtingudes de les diferents certificacions realitzades podran ajudar a desenvolupar eines i estratègies integrades d’aplicació de millores energètiques a nivell del parc d’edificis existent.

Intervention précoce dans la phase initiale des troubles psychotiques à Lausanne: quels problèmes et quelles solutions [Early intervention for the initial phase of psychotic disorders in Lausanne: what problems and what solutions?]

Schizophrenia has long been considered with pessimism, but the recent interest in the early phase of psychotic disorders has modified this often unjustified perception. Literature has demonstrated the benefit of the development of programs specialised in the treatment of early psychosis, which tend to be developed in many countries. It is however important to match them to local needs as well as to the structure of local health services. This paper reviews elements that justify such a development in Lausanne, Switzerland, and describe its various elements.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Volatility of Housing

The aim of the project is to develop a theoretical framework where homelessness arises due to various economic and social factors that vary over time. The ultimate goal is i) to understand whether homelessness spells, entrances and exits could be predicted and if so what information is necessary; and ii) to design and evaluate a homelessness prevention programme in a changing and uncertain environment. Examples of the questions we want to answer are: Should it be made easier for people to borrow money so that they can get out of homelessness, or will such borrowing allow people to over-consume today and so fall into homelessness tomorrow? Should precautionary savings be encouraged so that people have cushions to withstand future shocks, or will savings just delay entry into homelessness? What interventions will affect the probability of becoming homeless and how will they affect behaviour? How will interventions affect incentives to save and to consume before homelessness prevention programmes kick in?

Spatial Interactions in Hedonic Pricing Models: The Urban Housing Market of Aveiro, Portugal

Spatial heterogeneity, spatial dependence and spatial scale constitute key features of spatial analysis of housing markets. However, the common practice of modelling spatial dependence as being generated by spatial interactions through a known spatial weights matrix is often not satisfactory. While existing estimators of spatial weights matrices are based on repeat sales or panel data, this paper takes this approach to a cross-section setting. Specifically, based on an a priori definition of housing submarkets and the assumption of a multifactor model, we develop maximum likelihood methodology to estimate hedonic models that facilitate understanding of both spatial heterogeneity and spatial interactions. The methodology, based on statistical orthogonal factor analysis, is applied to the urban housing market of Aveiro, Portugal at two different spatial scales.

Social Housing Policies in Latin America and Singapore: Lessons for China

This paper addresses the challenges facing China in accelerating the pace of rural-urban migration as part of its on-going economic development programme. It explains the push and pull influences on migration and in particular explains why a continuing focus on urbanisation is justified by the very large gap between rural and urban incomes and the relatively higher income elasticity of demand for urban-based goods and services. The provision of affordable housing is an integral part of this structural shift programme. The paper thus considers the most appropriate ways in which housing finance can be mobilised, and thence how both the quality and the affordability of the housing stock can be increased. Positive and negative lessons for China are offered from the different urbanisation experiences of Latin America (especially Colombia) and Singapore.

An Investigation of Housing Affordability in the UK Regions

The housing market has been extensively investigated in the literature; however there is a lack of understanding of the fundamentals a ffecting housing affordability across UK regions as measured by the price to income ratio. The aim of this paper is twofold; fi rstly we calculate the a ffordability ratio based on individuals' incomes. Second we set o f to ask which socio-economic factors could a affect this ratio. The analysis finds a strong influence coming from the mortgage rate, the residents' age and academic quali fications. We also report a positive and signifi cant e ffect from foreign capital coming to the UK. Finally, we record a non-negligible degree of heterogeneity across the twelve regions.

Modelling Housing Prices using a Present Value State Space Model

This paper introduces a State Space approach to explain the dynamics of rent growth, expected returns and Price-Rent ratio in housing markets. According to the present value model, movements in price to rent ratio should be matched by movements in expected returns and expected rent growth. The state space framework assume that both variables follow an autoregressive process of order one. The model is applied to the US and UK housing market, which yields series of the latent variables given the behaviour of the Price-Rent ratio. Resampling techniques and bootstrapped likelihood ratios show that expected returns tend to be highly persistent compared to rent growth. The Öltered expected returns is considered in a simple predictability of excess returns model with high statistical predictability evidenced for the UK. Overall, it is found that the present value model tends to have strong statistical predictability in the UK housing markets.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Modelling Housing Prices using a Present Value State Space Model

This paper introduces a State Space approach to explain the dynamics of rent growth, expected returns and Price-Rent ratio in housing markets. According to the present value model, movements in price to rent ratio should be matched by movements in expected returns and expected rent growth. The state space framework assume that both variables follow an autoregression process of order one. The model is applied to the US and UK housing market, which yields series of the latent variables given the behaviour of the Price-Rent ratio. Resampling techniques and bootstrapped likelihood ratios show that expected returns tend to be highly persistent compared to rent growth. The filtered expected returns is considered in a simple predictability of excess returns model with high statistical predictability evidence for the UK. Overall, it is found that the present value model tends to have strong statistical predictability in the UK housing markets.