Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

On the general structure of gauged Wess-Zumino-Witten terms

The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit general expression for these cocycles is given. The common geometrical structure of the gauged closed forms and the D'Hoker and Weinberg effective actions of WZW type, as well as the obstructions for their existence, is also exhibited and explained.Comment: Some changes. 23 pages; latex2e file. To appear in Nucl. Phys.

Stochastic volatility and leverage effect

We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows us to fully estimate all parameters involved and it will entail a deeper study on correlated stochastic volatility models with practical applications on option pricing and risk management.Comment: 4 pages, 2 figure

Probability tree algorithm for general diffusion processes

Motivated by path-integral numerical solutions of diffusion processes, PATHINT, we present a new tree algorithm, PATHTREE, which permits extremely fast accurate computation of probability distributions of a large class of general nonlinear diffusion processes

Solving Electric Market Quadratic Problems by Branch and Fix Coordination Methods

The electric market regulation in Spain (MIBEL) establishes the rules for bilateral and futures contracts in the day-ahead optimal bid problem. Our model allows a price-taker generation company to decide the unit commitment of the thermal units, the economic dispatch of the bilateral and futures contracts between the thermal units and the optimal sale bids for the thermal units observing the MIBEL regulation. The uncertainty of the spot prices is represented through scenario sets. We solve this model on the framework of the Branch and Fix Coordination metodology as a quadratic two-stage stochastic problem. In order to gain computational efficiency, we use scenario clusters and propose to use perspective cuts. Numerical results are reportedPeer Reviewe

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Optimal Stopping and Losses on Subprime Mortgages

Lender losses on mortgage loans arise from a two-stage process. In the first stage, the borrower stops making payments if and when default is optimal. The second stage is a lengthy and costly period during which the lender employs legal remedies to obtain possession and execute a sale of the collateral. This research uses data on subprime mortgage losses to explore the role of borrower and collateral characteristics, and local legal requirements, as well as traditional option variables in the decisions of borrowers and lenders. Although subprime borrowers default earlier, which should reduce lender losses, these borrowers, nevertheless, impose greater realized losses on mortgage lenders.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47774/1/11146_2004_Article_4875.pd

Macroinvertebrate Diversity in Urban and Rural Ponds: Implications for Freshwater Biodiversity Conservation

Ponds are among the most biodiverse freshwater ecosystems, yet face significant threats from removal, habitat degradation and a lack of legislative protection globally. Information regarding the habitat quality and biodiversity of ponds across a range of land uses is vital for the long term conservation and management of ecological resources. In this study we examine the biodiversity and conservation value of macroinvertebrates from 91 lowland ponds across 3 land use types (35 floodplain meadow, 15 arable and 41 urban ponds). A total of 224 macroinvertebrate taxa were recorded across all ponds, with urban ponds and floodplain ponds supporting a greater richness than arable ponds at the landscape scale. However, at the alpha scale, urban ponds supported lower faunal diversity (mean: 22 taxa) than floodplain (mean: 32 taxa) or arable ponds (mean: 30 taxa). Floodplain ponds were found to support taxonomically distinct communities compared to arable and urban ponds. A total of 13 macroinvertebrate taxa with a national conservation designation were recorded across the study area and 12 ponds (11 floodplain and 1 arable pond) supported assemblages of high or very high conservation value. Pond conservation currently relies on the designation of individual ponds based on very high biodiversity or the presence of taxa with specific conservation designations. However, this site specific approach fails to acknowledge the contribution of ponds to freshwater biodiversity at the landscape scale. Ponds are highly appropriate sites outside of protected areas (urban/arable), with which the general public are already familiar, for local and landscape scale conservation of freshwater habitats

A robust spectral method for solving Heston’s model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979)

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa