Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging

We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta-vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas, and volgas of the non-traded and the liquidly traded options.Comment: 44 pages; forthcoming in 'Finance and Stochastics

Bootstrapping two-loop Feynman integrals for planar N=4 sYM

We derive analytic results for the symbol of certain two-loop Feynman integrals relevant for seven- and eight-point two-loop scattering amplitudes in planar $\mathcal{N}=4$ super-Yang--Mills theory. We use a bootstrap inspired strategy, combined with a set of second-order partial differential equations that provide powerful constraints on the symbol ansatz. When the complete symbol alphabet is not available, we adopt a hybrid approach. Instead of the full function, we bootstrap a certain discontinuity for which the alphabet is known. Then we write a one-fold dispersion integral to recover the complete result. At six and seven points, we find that the individual Feynman integrals live in the same space of functions as the amplitude, which is described by the 9- and 42-letter cluster alphabets respectively. Starting at eight points however, the symbol alphabet of the MHV amplitude is insufficient for individual integrals. In particular, some of the integrals require algebraic letters involving four-mass box square-root singularities. We point out that these algebraic letters are relevant at the amplitude level directly starting with N$^2$MHV amplitudes even at one loop.Comment: 49 page

The Regional Incidence of European Agricultural Policy: Measurement Concept and Empirical Evidence

Agricultural and Food Policy,

Minimum Race-Time Planning-Strategy for an Autonomous Electric Racecar

Increasing attention to autonomous passenger vehicles has also attracted interest in an autonomous racing series. Because of this, platforms such as Roborace and the Indy Autonomous Challenge are currently evolving. Electric racecars face the challenge of a limited amount of stored energy within their batteries. Furthermore, the thermodynamical influence of an all-electric powertrain on the race performance is crucial. Severe damage can occur to the powertrain components when thermally overstressed. In this work we present a race-time minimal control strategy deduced from an Optimal Control Problem (OCP) that is transcribed into a Nonlinear Problem (NLP). Its optimization variables stem from the driving dynamics as well as from a thermodynamical description of the electric powertrain. We deduce the necessary first-order Ordinary Differential Equations (ODE)s and form simplified loss models for the implementation within the numerical optimization. The significant influence of the powertrain behavior on the race strategy is shown.Comment: Accepted at The 23rd IEEE International Conference on Intelligent Transportation Systems, September 20 - 23, 202

Natural conditions in agriculture and the regional distribution of EU producer support

The redistributive implications of the Common Agricultural Policy (CAP) of the European Union (EU) have regained a strong interest in recent years since economic and social cohe-sion has become a major goal of European policy. The empirical evidence is surprisingly di-verse and ranges from a clearly positive to a clearly negative regional redistributive impact of the CAP. Therefore, the objectives of this paper are threefold. First, the interregional alloca-tion of EU producer support under the CAP is measured at the NUTS III-level in the period 1986-2002 for 26 regions of the German Bundesland Hesse. Second, the role of the measure-ment concept for the magnitude and distribution of the regional transfers is elaborated. Third, the interregional allocation of EU producer support is explained by natural conditions and farm structure variables within a quantitative analysis. A major result is that the interregional allocation of producer support is unequal, depends on the measure of protection used and is affected by a number of variables characterizing farm structure and natural conditions

Natural conditions in agriculture and the regional distribution of EU producer support

The redistributive implications of the Common Agricultural Policy (CAP) of the European Union (EU) have regained a strong interest in recent years since economic and social cohe-sion has become a major goal of European policy. The empirical evidence is surprisingly di-verse and ranges from a clearly positive to a clearly negative regional redistributive impact of the CAP. Therefore, the objectives of this paper are threefold. First, the interregional alloca-tion of EU producer support under the CAP is measured at the NUTS III-level in the period 1986-2002 for 26 regions of the German Bundesland Hesse. Second, the role of the measure-ment concept for the magnitude and distribution of the regional transfers is elaborated. Third, the interregional allocation of EU producer support is explained by natural conditions and farm structure variables within a quantitative analysis. A major result is that the interregional allocation of producer support is unequal, depends on the measure of protection used and is affected by a number of variables characterizing farm structure and natural conditions

Evolution of the electricity market in Germany: Identifying policy implications by an agent-based model

The diffusion of renewable electricity generating technologies is widely consid- ered as crucial for establishing a sustainable energy system in the future. However, currently the required transition is unlikely to be achieved by market forces alone. For this reason, many countries implement various policy instruments to support this process, also by re-distributing costs related to the policy instruments applied among all electricity consumers. This paper presents a novel history-friendly agent-based study aiming to explore efficiency of different mixes of policy instruments by means of a differential evolution algorithm. Special emphasis of the model is devoted to possibility of small scale renewable electricity generation without any further inputs, but also to storage of this electricity using small scale facilities being actively developed over the last decade. Both combined pose an important instrument to be used by electricity consumers to achieve partial or full autarky from the electricity grid, particularly after accounting for decreasing costs and increasing efficiency of both due to continuous innovation. Another distinct feature of this study is attention to stability of the electricity grid since more consumers becoming autarkic make, on the one hand, electricity in the grid more expansive, while on the other hand, supply of the electricity more vulnerable

Subsonic phase transition waves in bistable lattice models with small spinodal region

Phase transitions waves in atomic chains with double-well potential play a fundamental role in materials science, but very little is known about their mathematical properties. In particular, the only available results about waves with large amplitudes concern chains with piecewise-quadratic pair potential. In this paper we consider perturbations of a bi-quadratic potential and prove that the corresponding three-parameter family of waves persists as long as the perturbation is small and localised with respect to the strain variable. As a standard Lyapunov-Schmidt reduction cannot be used due to the presence of an essential spectrum, we characterise the perturbation of the wave as a fixed point of a nonlinear and nonlocal operator and show that this operator is contractive in a small ball in a suitable function space. Moreover, we derive a uniqueness result for phase transition waves with certain properties and discuss the kinetic relation.Comment: revised version with extended introduction, improved perturbation method, and novel uniqueness result; 20 pages, 5 figure