Knowledge-Capital Meets New Economic Geography

We incorporate the now standard knowledge-capital model of multinational firms in a new economic geography setting. The theoretical predictions of our model suggest that unskilled labor mobility leads to less concentration of production than skilled labor mobility does. This is in line with empirical evidence that agglomeration of production among European nations is less pronounced than among US regions. Our model shows that the different patterns in labor mobility can explain actual differences in the spreading of industries. According to our welfare analysis, trade liberalization is likely Pareto-improving for a larger (smaller) country with mobile unskilled (skilled) labor. In the supplement, we investigate the sensitivity of our results in several respects. In the first section, we provide the figures of real factor rewards for the trade liberalization scenarios discussed in and underlying Figures 7 and 8 of the paper. Second, in Figures 3(n) - 5(v) (6(n) - 6b(v)) we infer the existence, or non-existence, of each firm type separately in the τ - λ L-space (τ - λ S-space) for country i firms and all four scenarios of firm regimes. Third, we illustrate how changes in the parameters μ, ρ and σ affect the outcome. Finally, we analyze how the asymmetric endowment with the immobile factor influences the core-periphery patterns.knowledge-capital model, new economic geography, unskilled labor mobility, skilled labor mobility

The Berry-Keating operator on a lattice

We construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating

The Berry-Keating operator on a lattice

We construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating

On the exponential stability of uniformly damped wave equations

We study damped wave propagation problems phrased as abstract evolution equations in Hilbert spaces. Under some general assumptions, including a natural compatibility condition for initial values, we establish exponential decay estimates for all mild solutions using the language and tools of Hilbert complexes. This framework turns out strong enough to conduct our analysis but also general enough to include a number of interesting examples. Some of these are briefly discussed. By a slight modification of the main arguments, we also obtain corresponding decay results for numerical approximations obtained by compatible discretization strategies

Option Pricing using Quantum Computers

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu