Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility

The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems from one or more independent Poisson processes. Optimal behavior in such a setup (e.g., optimal consumption) is usually determined by employing the Hamilton-Jacobi-Bellman equation. This, however, requires strong assumptions on the model, such as a bounded utility function and bounded coefficients in the controlled differential equation. The present paper relaxes these assumptions. We show that one can still use the Hamilton-Jacobi-Bellman equation as a necessary criterion for optimality if the utility function and the coefficients are linearly bounded. We also derive sufficiency in a verification theorem without imposing any boundedness condition at all. It is finally shown that, under very mild assumptions, an optimal Markov control is optimal even within the class of general controls. --Stochastic differential equation,Poisson process,Bellman equation

"Ito's Lemma" and the Bellman equation for Poisson processes: An applied view

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman equation. This paper provides examples for the application of both tools in economic modeling. It accompanies the proofs in Sennewald (2005), who shows, under milder conditions than before, that the Hamilton-Jacobi-Bellman equation is both a necessary and sufficient criterion for optimality. The main example here consists of a consumption-investment problem with labor income. It is shown how the Hamilton-Jacobi-Bellman equation can be used to derive both a Keynes-Ramsey rule and a closed form solution. We also provide a new result. --Stochastic differential equation,Poisson process,Bellman equation,Portfolio optimization,Consumption optimization

“Itô’s Lemma“ and the Bellman Equation for Poisson Processes: An Applied View

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the proofs presented in the accompanying paper by Sennewald (2006). Additional examples are given which highlight the correct use of the Hamilton-Jacobi-Bellman equation and the change-of-variables formula (sometimes referred to as “Ito’s-Lemma”) under Poisson uncertainty.stochastic differential equation, Poisson process, Bellman equation, portfolio optimization, consumption optimization

"Itô's Lemma" and the Bellman equation: An applied view

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman equation. This paper provides examples for the application of both tools in economic modeling. It accompanies the proofs in Sennewald (2005), who shows, under milder conditions than before, that the Hamilton-Jacobi-Bellman equation is both a necessary and sufficient criterion for optimality. The main example here consists of a consumption-investment problem with labor income. It is shown how the Hamilton-Jacobi-Bellman equation can be used to derive both a Keynes-Ramsey rule and a closed form solution. We also provide a new result. --Stochastic differential equation,Poisson process,Bellman equation,Portfolio optimization,Consump

The Nexus of Federal and State Law in Railroad Abandonments

The United States Congress embarked on a new era in the regulation of interstate commerce when it created the Interstate Commerce Commission ( ICC ) in 1887 to regulate railroad traffic.\u27 A major purpose of the ICC regulatory framework, as amended by the Transportation Act of 1920, was to preempt actions by state and local authorities that prevented railroads from abandoning unprofitable lines. When Congress passed the Transportation Act, 252,588 miles of track criss-crossed the United States; by 1990 the number of rail- way miles had decreased by almost half. Although the relative ease with which railroads abandoned unprofitable lines augmented their profitability, state and local governments realized that corridors assembled in the mid-nineteenth century were extremely expensive to reassemble once abandoned. Local authorities began considering other public uses for railroad rights-of-way, such as roads or highways, the placement of utility lines, or recreational trails. In an effort to conserve railway corridors as a national resource, both for future transportation use and for current use as recreational trails, Congress included unique provisions within the Railroad Revitalization and Regulatory Reform Act of 1976 ( 4-R Act ) and the National Trails Systems Act Amendments of 1983 ( Rails-to-Trails Act ). Specifically, the Rails-to-Trails Act asserted federal control over the disposition of abandoned railroad rights-of-way and promoted alternative uses for railway corridors. The abandonment of rail service on a railway line requires the approval of the Surface Transportation Board ( STB ), the successor to the ICC. Until the STB grants such approval, the railway line is considered part of the national transportation system. The requirement of STB approval can present a direct conflict with state property law. What is the result when a railroad right-of-way, held by the railroad in the form of an easement, has purportedly been abandoned under state property law before the STB has given permission to abandon rail service? Does the easement terminate, thereby dispossessing the railroad (or the railroad\u27s successor) of its property interest, or does federal law perpetuate the easement under the jurisdiction of the STB, thus preserving the right-of-way for future transportation use? If the easement continues to exist, does the establishment of a recreational trail upon the railroad easement constitute a taking under the Fifth Amendment? This Note addresses these questions and advocates, despite a recent Federal Circuit Court of Appeals decision to the contrary, that railroad rights-of-way should not be considered abandoned pursuant to state property law while the rail corridor is still subject to the jurisdiction of the STB. The proposition that federal law preempts state law in this situation is supported by explicit congressional intent to subordinate state property law, and is founded on the Supremacy Clause and the federal government\u27s power to regulate interstate commerce under the Commerce Clause. In addition, this Note concludes that the perpetuation by federal law of an easement underlying a railroad right-of-way-and the establishment of a recreational trail upon the easement-should not constitute a taking of property from the owner of the servient estate under the Fifth Amendment

Alien Gender: Die Inszenierung von Geschlecht in Science-Fiction-Serien

"Ma'am Captain", Action Girls und Dritte Geschlechter - die Studie beschäftigt sich mit der Inszenierung von Geschlecht in der populären Kultur am Beispiel von sechs Science-Fiction-Serien. Das hegemoniale Bild heldischer Männlichkeit wird nach wie vor reproduziert, gleichzeitig treten auch neue, weibliche Figurentypen auf. Anhand geschlechtsspezifisch kodierter Themen wie Macht, Autorität, Gewalt, Partnerschaft, Sexualität und Elternschaft werden die narrativen und visuellen Strategien der Geschlechterinszenierung beleuchtet. Die Methodik und die Ergebnisse der Studie sind gut auf die Analyse anderer Film- und Fernsehgenres übertragbar

Ungleich, aber gerecht? Legitimationsangebote für Ungleichheit in der Frankfurter Allgemeinen Zeitung seit 1970

An der Notwendigkeit und Legitimität von bestehenden Ungleichheiten zweifeln ernsthaft nur die wenigsten Menschen. In der aufstiegsorientierten Mittelschicht finden neoliberale Argumente und die damit einhergehenden Legitimationsmuster trotz Krisenstimmung und Abstiegsängsten weiterhin breite Zustimmung. Diese Legitimationsmuster werden in der (Medien-)Gesellschaft durch JournalistInnen und PublizistInnen, in ihrer Funktion als „Legitimatoren“  bzw. „organische Intellektuelle“ weitergegeben. Antonio Gramsci folgend fällt diesen darüber hinaus die Aufgabe zu, sich Kompromisse zwischen den extremen Lösungen auszudenken, um moderatere, anschlussfähigere Meinungen zu schaffen. Die Auseinandersetzung damit, welche Legitimationsangebote die Frankfurter Allgemeine Zeitung (FAZ) ihrem Publikum in Bezug auf soziale Ungleichheit und die ideologische Entkopplung von Gleichheit und Gerechtigkeit seit den 1970er Jahren gemacht hat, bildet den Kern der vorliegenden Untersuchung

Schreiben, Reflektieren, Kommunizieren

Was fördert Schreibprozesse, was behindert sie? In ihrer explorativen und interdisziplinären Studie erkundet die Autorin Schreibprozesse aus der Perspektive Studierender. Empirische Grundlage sind umfangreiche schriftliche Selbstaussagen. Nach einer wissenschaftlichen Verortung der Studie analysiert die Autorin die Daten anhand der Grounded-Theory-Methode in unterschiedlichen Richtungen: Ebenen, auf denen aus der Perspektive der Schreibenden Reibungsverluste beim Schreiben entstehen sowie Faktoren, die den Schreibprozess fördern oder Störungen beseitigen. Dabei zeigt sich die Fähigkeit zur Reflexion als zentrale Kompetenz, die anhand unterschiedlicher theoretischer Konstrukte vergleichend diskutiert und gerahmt wird. Am Beispiel von Schreibstrategien und des Adressatenbewusstseins untersucht die Autorin, wie Reflexion aus der Perspektive der Schreibenden auf unterschiedlichen Ebenen des Schreibprozesses wirkt. Aus den Ergebnissen leitet die Autorin erste Thesen für eine reflexionsorientierte Schreibdidaktik ab, die zu Diskussion, Forschung und zur Weiterentwicklung didaktischer Konzepte einladen sollen