Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology

We model equilibrium spot and futures oil prices in a general equilibrium production economy. In our model production of the consumption good requires two inputs: the consumption good and a commodity, e.g., Oil. Oil is produced by wells whose flow rate is costly to adjust. Investment in new Oil wells is costly and irreversible. As a result in equilibrium, investment in Oil wells is infrequent and lumpy. Even though the state of the economy is fully described by a one-factor Markov process, the spot oil price is not Markov (in itself). Rather it is best described as a regime-switching process, the regime being an investment `proximity' indicator. The resulting equilibrium oil price exhibits mean-reversion and heteroscedasticity. Further, the risk premium for exposure to commodity risk is time-varying, positive in the far-from-investment regime but negative in the near-investment regime. Further, our model captures many of the stylized facts of oil futures prices, such as backwardation and the `Samuelson effect.' The futures curve exhibits backwardation as a result of a convenience yield, which arises endogenously. We estimate our model using the Simulated Method of Moments with economic aggregate data and crude oil futures prices. The model successfully captures the first two moments of the futures curves, the average non-durable consumption-output ratio, the average oil consumption-output and the average real interest rate. The estimation results suggest the presence of convex adjustment costs for the investment in new oil wells. We also propose and test a linear approximation of the equilibrium regime-shifting dynamics implied by our model, and test its empirical implication for time-varying risk-premia.

On the convergence of densities of finite voter models to the Wright-Fisher diffusion

We study voter models defined on large sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright-Fisher diffusion only involves certain averages of the voter models over a small number of spatial locations. This enables us to identify suitable mixing conditions on the underlying voting kernels, one of which may just depend on their eigenvalues in some contexts, to obtain the convergence of density processes. Our examples show that these conditions are satisfied by a large class of voter models on growing finite graphs

Rayleigh random flights on the Poisson line SIRSN

We study scale-invariant Rayleigh Random Flights (“RRF”) in random environments given by planar Scale-Invariant Random Spatial Networks (“SIRSN”) based on speed-marked Poisson line processes. A natural one-parameter family of such RRF (with scale-invariant dynamics) can be viewed as producing “randomly-broken local geodesics” on the SIRSN; we aim to shed some light on a conjecture that a (non-broken) geodesic on such a SIRSN will never come to a complete stop en route. (If true, then all such geodesics can be represented as doubly-infinite sequences of sequentially connected line segments. This would justify a natural procedure for computing geodesics.) The family of these RRF (“SIRSN-RRF”), is introduced via a novel axiomatic theory of abstract scattering representations for Markov chains (itself of independent interest). Palm conditioning (specifically the Mecke-Slivnyak theorem for Palm probabilities of Poisson point processes) and ideas from the ergodic theory of random walks in random environments are used to show that at a critical value of the parameter the speed of the scale-invariant SIRSN-RRF neither diverges to infinity nor tends to zero, thus supporting the conjecture

Scan Quantum Mechanics: Quantum Inertia Stops Superposition

A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible: decreasing the size, temperature, gravitational force, etc. of a classical system one could revert the situation. Entanglement can only occur between quantum systems, not between a quantum system and a classical one, because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia $I_{cr}$ corresponding to different observables. In addition, our proposal implies a new radiation mechanism in strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.Comment: 30 pages, no figures. Many improvements in the presentation, including contents and a table, several references added. Ideas unchange

Electrowetting: from basics to applications

Electrowetting has become one of the most widely used tools for manipulating tiny amounts of liquids on surfaces. Applications range from 'lab-on-a-chip' devices to adjustable lenses and new kinds of electronic displays. In the present article, we review the recent progress in this rapidly growing field including both fundamental and applied aspects. We compare the various approaches used to derive the basic electrowetting equation, which has been shown to be very reliable as long as the applied voltage is not too high. We discuss in detail the origin of the electrostatic forces that induce both contact angle reduction and the motion of entire droplets. We examine the limitations of the electrowetting equation and present a variety of recent extensions to the theory that account for distortions of the liquid surface due to local electric fields, for the finite penetration depth of electric fields into the liquid, as well as for finite conductivity effects in the presence of AC voltage. The most prominent failure of the electrowetting equation, namely the saturation of the contact angle at high voltage, is discussed in a separate section. Recent work in this direction indicates that a variety of distinct physical effects¿rather than a unique one¿are responsible for the saturation phenomenon, depending on experimental details. In the presence of suitable electrode patterns or topographic structures on the substrate surface, variations of the contact angle can give rise not only to continuous changes of the droplet shape, but also to discontinuous morphological transitions between distinct liquid morphologies. The dynamics of electrowetting are discussed briefly. Finally, we give an overview of recent work aimed at commercial applications, in particular in the fields of adjustable lenses, display technology, fibre optics, and biotechnology-related microfluidic devices

Stochastic optimal control and regime switching : applications in economics

Economic decisions under uncertainty generally involve a change of stochastic regime. This thesis examines the formal conditions for optimizing such decisions and looks at applications to exchange rate intervention, physical investment and consumption behaviour. Many of these economic regime switchings can be mathematically formulated as stopping problems. Global optimality is achieved by applying Hamilton-Jacobi-Bellman equations in each regime, together with the joining conditions at the switching boundaries. Chapter 1 establishes the framework for optimisation and provides various boundary conditions for different switching cases. Chapter 2 applies optimal stopping techniques to derive optimal “time-consistent” exchange rate target zones in the presence of proportional/lump sum intervention costs. It further shows that such discretionary equilibria can be improved upon by a credible commitment to an exchange rate mechanism (such as ERM). Chapter 3 characterises the irreversible oil investment decision in the North Sea as an optimal regime switching problem. In the absence of Petroleum Revenue Tax (PRT), it shows how the optimal development decision will be deferred when real oil prices follow a geometric Brownian motion. In chapter 4, an intertemporal partial equilibrium model of investment is used to assess the effects of stochastic capital depreciation on optimal investment behaviour, in a context where a sales constraint effectively decomposes the problem into two distinct regimes. The presence of the uncertainty about depreciation reduces firm’s demand for investment; and increasing the variability of capital depreciation further reduces investment. The uncertainty also makes investment “smoother” than that under certainty. Finally, chapter 5 and 6 deal with optimal consumption/portfolio decisions in a two-asset model with shortselling and borrowing restrictions imposed. Chapter 5 formulates a regime switching problem due to the presence of the borrowing constraint and specifies the corresponding boundary conditions. Chapter 6 characterises optimal solutions to various combinations of parameters for constant relative and constant absolute risk aversion utility functions. In many cases, if labour income is fully diversifiable, the borrowing constraint only binds when the wealth level falls below a threshold, and risk taking behaviour at the low level of wealth is associated with a convex portion of the indirect utility function (value function). In such regime-switch cases, the introduction of the borrowing constraint makes consumption more volatile relative to income. It also generates the precautionary motive for saving

On two-sided controls of a linear diffusion

siirretty Doriast

Novel spin functionalities of C60 based metallo-molecular interfaces

Novel functionalities of C60-based interfaces are investigated with the aim of controlling induced spin-dependent phenomena through electrical and optical charging in photovoltaic devices and the generation of spin-triplet correlations in magneto-molecular/superconductor proximity systems. Low-energy muon spin rotation is used to probe local magnetic field distributions in molecule/metal-oxide heterojunctions. It is shown that the population of interfacial traps after electrical and optical charging produces an induced magnetisation due to the spin-splitting of the interface. This is supported by XAS and XMLD measurements in similar systems. The emergence of a peak at 282 eV, often associated with interfacial hybridisation, after an electrical bias shows a magnetic field dependence in its X-ray linear dichroism. We propose how these effects may be reversibly switched on and off through the tuning of the interfacial chemistry via electromigration of oxygen in the device. In Nb/C60 stacks a superconducting state can be induced in the molecular layer via the proximity effect. The incorporation of weakly magnetic Cu/C60 interfaces leads to the emergence of a paramagnetic spin susceptibility in the superconducting state, as probed by low-energy muon spin rotation. We attribute this effect to the generation of odd-frequency spin-triplet correlations at the spin-split Cu/C60 interface. These studies are a demonstration of novel device architectures available to the field of molecular spintronics. Utilising the unique spin-dependent phenomena observed in hybrid molecular interfaces, systems with new functionalities can be designed