Mortgage Rate Pass-Through in Switzerland

This paper investigates the speed and completeness of the pass-through from market rates to mortgage rates in Switzerland. The pass-through dynamics are studied under a marginal funding cost perspective. By choosing the appropriate benchmark rates, this study takes into account banks' forecasts of the evolution of their funding costs. It is found that the passthrough of rates of adjustable-rate mortgages is incomplete and sluggish compared to the rates of mortgages with a fixed maturity. For the latter, changes in market rates appear to be transmitted quickly and completely, particularly when benchmark rates are falling. This finding suggests that a low-interest-rate environment stimulates competition among financial institutions. Evidence for a structural change is found for all interest rates. The structural change occurred around the beginning of 2007 for fixed-rate mortgages and in mid-2005 for floating-rate mortgages. For all mortgage rates, asymmetries are detected in the pre-break period. More specifically, the adjustment of fixed-rate-mortgage rates is characterized by downward rigidity, which supports the existence of some form of imperfect competition. By contrast, the rates of adjustable-rate mortgages exhibit upward price stickiness. This result suggests that competition was stronger in this specific mortgage-lending market. In the post-break period, no clear evidence is found in favor of asymmetries with respect to the adjustment coefficient.Interest Rate Pass-Through, Monetary Policy, Mortgages, Cointegration analysis, Panel Data

Convergence, Fluctuations and Large Deviations for finite state Mean Field Games via the Master Equation

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled forward-backward ODEs. We exploit the so-called Master Equation, which in this finite-dimensional framework is a first order PDE in the simplex of probability measures, obtaining the convergence of the feedback Nash equilibria, the value functions and the optimal trajectories. The convergence argument requires only the regularity of a solution to the Master equation. Moreover, we employ the convergence method to prove a Central Limit Theorem and a Large Deviation Principle for the evolution of the N-player empirical measures. The well-posedness and regularity of solution to the Master Equation are also studied

Il contributo della SIS Piemonte alla didattica disciplinare

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On the convergence problem in Mean Field Games: a two state model without uniqueness

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the master equation possesses a smooth solution which can be used to prove convergence of the value functions and of the feedback Nash equilibria of the N-player game, as well as a propagation of chaos property for the associated optimal trajectories. We study here an example with anti-monotonous costs, and show that the mean field game has exactly three solutions. We prove that the value functions converge to the entropy solution of the master equation, which in this case can be written as a scalar conservation law in one space dimension, and that the optimal trajectories admit a limit: they select one mean field game soution, so there is propagation of chaos. Moreover, viewing the mean field game system as the necessary conditions for optimality of a deterministic control problem, we show that the N-player game selects the optimizer of this problem

Study of molecular mechanisms to increase carbon use efficiency in microalgae

In order to better understand alga\u2019s biology and allow to design biotechnological approaches to improve biomass yield, in this PhD thesis we investigated the molecular mechanism involved in the microalgae carbon use efficiency. In the Chapter 1 we studied the model algae C. reinhardtii. In section A Photosystem II assembly were investigated. Indeed, no detailed studies of the assembly factors of PSII have been performed. In this work we focus on a putative assembly factor of the CP43 subunit, called LPA2 (low PSII accumulation 2), previously identified in A. thaliana. A candidate lpa2 gene in C. reinhardtii was identified by homology and its role was studied in vivo thank to a CRISPR-cas9 mutant. The data collected demonstrated that LPA2 protein is involved in both de novo biogenesis and repair of PSII. In the section B the relationship between chloroplast and mitochondrion metabolism was explored studying a mutant of C. reinhardtii knockout for a mitochondrial transcription factor. Previous studies demonstrated that the mutation affect the mitochondrial respiration and resulted in a light-sensitive phenotype. In this work we investigated how a mutation affecting the mitochondrial respiration perturbed light acclimation of the strain. Chapter 2 regards two species of Chlorella genus. In the section A we elucidated the molecular basis of the improved growth and biomass yield in mixotrophic condition, where the cross-talk between chloroplast and mitochondria metabolism is essential for efficient biomass production. C. sorokiniana is able to combine an autotrophic metabolism with the utilization of reduced carbon source (mixotrophic condition). The de novo assembly transcriptome allowed to identify the regulation of several genes involved in control of carbon flux. In section B genetic basis of the highly productive phenotype of C. vulgaris in low light vs. high light condition was examined. Nuclear and organelle genomes were obtained combining short-reads Illumina, long PacBio reads and Bionano optical mapping, allowing to assembly a near-chromosome scale genome of 14 scaffolds and the two complete circular organelle genomes. All the genes encoding for photosynthetic subunit, as well as, genes involved in the key metabolic pathway were identified. In section C the two Chlorella species was compared for their adaptation to high CO2 level. In C. sorokiniana in 3% CO2 were observed several reorganizations of the photosynthetic machinery leading to an improved carbon fixation, while mitochondrial respiration was essentially unaffected. Instead, in C. vulgaris the 3% CO2 induced an improved uptake of reducing power by chloroplast leading to a reduced mitochondrial respiration. Chapter 3 is focused on the marine algae. In the section A was isolated a chemical mutant of N. gaditana with a reduction chlorophyll content per cell combined with increased lipids productivity. The mutant did not show an increased biomass accumulation but induced an increased lipid content, a class of macromolecules with a higher energy content per gram. This is in any case an indication of improved light energy conversion in line with an improved light penetration in the photobioreactor and more homogenous light availability due to the reduced chlorophyll content per cell in the mutant. Moreover, thank to Illumina sequencing, we found putative genes responsible of the observed phenotype. In the section B cells of T. weissflogii were grown together with an artificial cyanine molecular antenna (Cy5) that extends the absorbance range of the photosynthetic apparatus exploiting light energy in the orange spectral region. The dye was incorporate in the algae increasing light dependent growth, oxygen and biomass production. Time-resolved spectroscopy data indicates that a Cy5-chlorophyll a energy transfer mechanism happen, compatible with a FRET process

Probabilistic Approach to Finite State Mean Field Games

We study mean field games and corresponding N-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we use a probabilistic representation of the system dynamics in terms of stochastic differential equations driven by Poisson random measures. Under mild assumptions, we prove existence of solutions to the mean field game in relaxed open-loop as well as relaxed feedback controls. Relying on the probabilistic representation and a coupling argument, we show that mean field game solutions provide symmetric \u3b5_N-Nash equilibria for the N-player game, both in open-loop and in feedback strategies (not relaxed), with \u3b5_N 64constant 1aN. Under stronger assumptions, we also find solutions of the mean field game in ordinary feedback controls and prove uniqueness either in case of a small time horizon or under monotonicity

Weak solutions to the master equation of potential mean field games

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without any monotonicity constraint on the coefficients. The key point is to interpret the master equation in a conservative sense and then to adapt to the infinite dimensional setting earlier arguments for hyperbolic systems deriving from a Hamilton-Jacobi-Bellman equation. Here, the master equation is indeed regarded as an infinite dimensional system set on the space of probability measures and is formally written as the derivative of the Hamilton-Jacobi-Bellman equation associated with the mean field control problem lying above the mean field game. To make the analysis easier, we assume that the coefficients are periodic, which allows to represent probability measures through their Fourier coefficients. Most of the analysis then consists in rewriting the master equation and the corresponding Hamilton-Jacobi-Bellman equation for the mean field control problem as partial differential equations set on the Fourier coefficients themselves. In the end, we establish existence and uniqueness of functions that are displacement semi-concave in the measure argument and that solve the Hamilton-Jacobi-Bellman equation in a suitable generalized sense and, subsequently, we get existence and uniqueness of functions that solve the master equation in an appropriate weak sense and that satisfy a weak one-sided Lipschitz inequality. As another new result, we also prove that the optimal trajectories of the associated mean field control problem are unique for almost every starting point, for a suitable probability measure on the space of probability measures