Single Jump Processes and Strict Local Martingales

Many results in stochastic analysis and mathematical finance involve local martingales. However, specific examples of strict local martingales are rare and analytically often rather unhandy. We study local martingales that follow a given deterministic function up to a random time $\gamma$ at which they jump and stay constant afterwards. The (local) martingale properties of these single jump local martingales are characterised in terms of conditions on the input parameters. This classification allows an easy construction of strict local martingales, uniformly integrable martingales that are not in $H^1$, etc. As an application, we provide a construction of a (uniformly integrable) martingale $M$ and a bounded (deterministic) integrand $H$ such that the stochastic integral $H\bullet M$ is a strict local martingale.Comment: 21 pages; forthcoming in 'Stochastic Processes and their Applications

Minimal Conditions for Implications of Gronwall-Bellman Type

Gronwall-Bellman type inequalities entail the following implication: if a sufficiently integrable function satisfies a certain homogeneous linear integral inequality, then it is nonpositive. We present a minimal (necessary and sufficient) condition on the Borel measure underlying the integrals for this implication to hold. The condition is also a necessary prerequisite for any nontrivial bound on solutions to inhomogeneous linear integral inequalities of Gronwall-Bellman type.Comment: 11 pages; forthcoming in 'Journal of Mathematical Analysis and Applications

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

The Behavior of Spontaneous Volunteers: A Discrete Choice Experiment on the Decision to Help

Modern communication technology has enabled new ways to exchange information and is one of the main drivers for citizens’ participation in disaster response. During the last decades, so-called spontaneous volunteers have become an important resource in coping with disasters. However, their unpredictable behavior has also led to several problems. Disaster managers urgently need insights into volunteers’ behavior to effectively use the offered potential. To gain and provide these insights into explaining what drives the decision to help, we performed a discrete choice experiment based on previously identified behavior-affecting attributes. Our results indicate that attributes like the scale of the disaster and the media coverage are among the most important factors in the decision to help. The model correctly predicts volunteers’ scenario-specific decisions with an accuracy of 65\%. Hence, the experiment offers valuable insights into volunteers’ behaviors for disaster research and is a sound foundation for decision support for disaster management

PageRank centrality for performance prediction: the impact of the local optima network model

A local optima network (LON) compresses relevant features of fitness landscapes in a complex network, where nodes are local optima and edges represent transition probabilities between different basins of attraction. Previous work has found that the PageRank centrality of local optima can be used to predict the success rate and average fitness achieved by local search based metaheuristics. Results are available for LONs where edges describe either basin transition probabilities or escape edges. This paper studies the interplay between the type of LON edges and the ability of the PageRank centrality for the resulting LON to predict the performance of local search based metaheuristics. It finds that LONs are stochastic models of the search heuristic. Thus, to achieve an accurate prediction, the definition of the LON edges must properly reflect the type of diversification steps used in the metaheuristic. LONs with edges representing basin transition probabilities capture well the diversification mechanism of simulated annealing which sometimes also accepts worse solutions that allow the search process to pass between basins. In contrast, LONs with escape edges capture well the diversification step of iterated local search, which escapes from local optima by applying a larger perturbation step

Development and Performance Verification of the GANDALF High-Resolution Transient Recorder System

With present-day detectors in high energy physics one often faces fast analog pulses of a few nanoseconds length which cover large dynamic ranges. In many experiments both amplitude and timing information have to be measured with high accuracy. Additionally, the data rate per readout channel can reach several MHz, which leads to high demands on the separation of pile-up pulses. For an upgrade of the COMPASS experiment at CERN we have designed the GANDALF transient recorder with a resolution of 12bit@1GS/s and an analog bandwidth of 500\:MHz. Signals are digitized with high precision and processed by fast algorithms to extract pulse arrival times and amplitudes in real-time and to generate trigger signals for the experiment. With up to 16 analog channels, deep memories and a high data rate interface, this 6U-VME64x/VXS module is not only a dead-time free digitization unit but also has huge numerical capabilities provided by the implementation of a Virtex5-SXT FPGA. Fast algorithms implemented in the FPGA may be used to disentangle possible pile-up pulses and determine timing information from sampled pulse shapes with a time resolution better than 50 ps.Comment: 5 pages, 9 figure

Historicization without periodization: post-postmodernism and the poetics of politics

A large number of recent scholarship in (American) literary and cultural studies is devoted to describing the contemporary moment as a monumental break from the previous (or current) period, postmodernism, by hailing our contemporary times as the era of post-postmodernism, late postmodernism, metamodernism, cosmodernism, or of a similarly termed construction. In these different proclamations, we recognize a pervasive tendency to periodize, an attempt to separate phases of human existence and cultural creation into neat stages that ‘logically’ follow after one another to form a supposedly coherent narrative. This practice of periodizing comes with a number of pitfalls that many of these studies seem not fully aware of, and it in turn speaks to (and characterizes) the contemporary moment as one marked by a desire for the boundedness of such clear divisions. In the following pages, we chronicle the quandaries that follow from such implicit and explicit efforts of periodization by focalizing them through three different ‘creation myths’ of the contemporary that such efforts at periodization typically subscribe to. As a way of sidestepping these, we accentuate the strengths of more ‘local’ critical lenses, approaches that historicize without periodizing. As one such lens, we suggest to engage the contemporary moment through the ‘poetics of politics,’ a historical discursive formation in which literary and popular texts’ desire for political relevance is matched by a recognition, in politics, of the (meta)textual quality of political action