From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments

We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous structure as the Black-Scholes model, the widely popular option pricing model in stochastic finance, for both European and American options with convex payoffs. In the case of non-convex options, we construct approximate pricing algorithms, and demonstrate that their efficiency can be analyzed through the introduction of an artificial probability measure, in parallel to the so-called risk-neutral measure in the finance literature, even though our framework is completely adversarial. Continuous-time convergence results and extensions to incorporate price jumps are also presented

No Laplacian Perfect State Transfer in Trees

We consider a system of qubits coupled via nearest-neighbour interaction governed by the Heisenberg Hamiltonian. We further suppose that all coupling constants are equal to $1$. We are interested in determining which graphs allow for a transfer of quantum state with fidelity equal to $1$. To answer this question, it is enough to consider the action of the Laplacian matrix of the graph in a vector space of suitable dimension. Our main result is that if the underlying graph is a tree with more than two vertices, then perfect state transfer does not happen. We also explore related questions, such as what happens in bipartite graphs and graphs with an odd number of spanning trees. Finally, we consider the model based on the $XY$-Hamiltonian, whose action is equivalent to the action of the adjacency matrix of the graph. In this case, we conjecture that perfect state transfer does not happen in trees with more than three vertices.Comment: 15 page

Free Entry in a Cournot Market with Imperfectly Substituting Goods

Two results are shown about the free-entry equilibrium in a Cournot market with asymmetric firms and imperfectly substituting goods. First, only one technology will survive in the production of each good. Second, some good(s) may not be produced. Specifically, we show that in a two-good model only one good is produced if the substitution parameter is higher than a critical value and both goods are produced for smaller substitution parameter values.Free-entry equilibrium; Cournot competition; substituting goods

Perception of Waiting Time at Signalized Intersections

Perceived waiting time at signalized intersections differs from the real value, and varies with signal design. The onerousness of delay depends on the conditions under which it is experienced. Using weighted travel time time may contribute to optimal signal control if its use can improve upon assuming that all time is weighted equally by users. This research explores the perception of waiting time at signalized intersections based on the results of an online survey, which directly collected the perceived waiting time and the user ratings of the signal designs of each intersection on an arterial including 3 intersections. Statistically analyzing the survey data suggests the perception of waiting time is a function of the real time; and a quadratic model better can describes relationship. The survey also indicates that there exists a tradeoff between the total waiting time and the individual waiting time of each intersection. It turns out that drivers prefer to split the total waiting time at different intersections at the price of a longer total wait if the difference of the total waiting time of two signal designs is within 30 seconds. The survey data shows that the perceived waiting time, instead of the real waiting time, better explains how users will rate the individual signal designs for both intersections and arterials including multiple intersections.Traffic Signal, Stated Preference, Virtual Experience Stated Preference, Signalized Intersection, Value of Time, Perception of Time

The preparation of crystalline lactic acid

On account of its importance in intermediary metabolism, lactic acid was among the first compounds chosen in our plan, which we have described in a previous communication (1), to augment the available data on the free energies of formation of substances significant in biological chemistry. It was necessary for this purpose to obtain pure crystalline lactic acid, free of water, anhydride, and lactide. The only description in the literature of the preparation of crystalline lactic acid is that of Krafft and Dÿes (2). Table I shows that the product obtained by their method contains relatively large quantities of anhydro impurities. The subject of the present communication is the description of a method which yields the active isomers of lactic acid in a crystalline state, free of water, anhydride, and lactide, supplemented by the description of two methods of separating the active forms from the commercial syrup (1). Lactic acid commercially available at present either is in the form of the U.S.P. syrup, which usually exhibits a low optical activity corresponding to the excess it happens to contain, which is variable, of one or the other optical isomer, or is the expensive zinc sarcolactate. The methods described below now make it possible to obtain easily and quickly and at low cost large quantities of both active isomers in a relatively high degree of purity

Measuring Winners and Losers from the new I-35W Mississippi River Bridge

The opening of the replacement for the I-35W Mississippi River Bridge bridge on September 18th, 2008 provides a unique opportunity to evaluate the impacts generated by this additional link on network performance, and thus empirically test whether a Braess Paradox occurred. Using detailed GPS data to estimate travel times on links and for origin-destination pairs, this research Þnds that while on average travel time improved with the reopening of the bridge, the subsequent restoration of parts of the rest of the network to their pre-collapse conÞguration worsened travel times signiÞcantly on average. In all cases, the distribution of winners and losers indicates clear spatial patterns associated with these network changes. While no Braess paradox was found in this case, the research provides a method for measuring such phenomena.Network structure, travel behavior, transport geography, commuting, network disruption, Braess paradox

Engaging Undergraduate Students in Transportation Studies through Simulating Transportation for Realistic Engineering Education and Training (STREET)

The practice of transportation engineering and planning has evolved substantially over the past several decades. A new paradigm for transportation engineering education is required to better engage students and deliver knowledge. Simulation tools have been used by transportation professionals to evaluate and analyze the potential impact of design or control strategy changes. Conveying complex transportation concepts can be effectively achieved by exploring them through simulation. Simulation is particularly valuable in transportation education because most transportation policies and strategies in the real world take years to implement with a prohibitively high cost. Transportation simulation allows learners to apply different control strategies in a risk-free environment and to expose themselves to transportation engineering methodologies that are currently in practice. Despite the advantages, simulation, however, has not been widely adopted in the education of transportation engineering. Using simulation in undergraduate transportation courses is sporadic and reported efforts have been focused on the upper-level technical elective courses. A suite of web-based simulation modules was developed and incorporated in the undergraduate transportation courses at University of Minnesota. The STREET (Simulating Transportation for Realistic Engineering Education and Training) research project was recently awarded by NSF (National Science Foundation) to develop web-based simulation modules to improve instruction in transportation engineering courses and evaluate their effectiveness. Our ultimate goal is to become the epicenter for developing simulation-based teaching materials, an active textbook, which offers an interactive learning environment to undergraduate students. With the hand-on nature of simulation, we hope to improve student understanding of critical concepts in transportation engineering and student motivation toward transportation engineering, and improve student retention in the field. We also would like to disseminate the results and teaching materials to other colleges to integrate the simulation modules in their curricula.Transportation Education and Training, Transportation Simulation, Roadway Geometry Design