Existence of optimal stationary policies in deterministic optimal control

AbstractThis paper considers deterministic discrete-time optimal control problems over an infinite horizon involving a stationary system and a nonpositive cost per stage. Various results are provided relating to existence of an ϵ-optimal stationary policy, and existence of an optimal stationary policy assuming an optimal policy exists

Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure

Boys and their toys : status inconsistency in non-democratic regimes and the import of major weapon systems

Major weapon system imports are significant as they are useful for domestic and international security. However, states regularly imported weapons they want in addition to weapons they need. One explanation is that states import unnecessary weapons to gain status. We argue that states suffering from higher levels of negative status inconsistency (SI) import a greater proportion of status symbol weapons. To account for differing security motives, we also separate non-democratic regime types – strongman, junta, boss, and machine – as they vary in their international conflict propensity and domestic stability. Due to the differences across these regimes, we further argue that non-democratic personalist regimes will import more status symbol weapons. Using data covering 1965–1999, we find that negatively status inconsistent regimes import more status symbol weapons

Metatranscriptomic profiles of Eastern subterranean termites, Reticulitermes flavipes (Kollar) fed on second generation feedstocks

Background: Second generation lignocellulosic feedstocks are being considered as an alternative to first generation biofuels that are derived from grain starches and sugars. However, the current pre-treatment methods for second generation biofuel production are inefficient and expensive due to the recalcitrant nature of lignocellulose. In this study, we used the lower termite Reticulitermes flavipes (Kollar), as a model to identify potential pretreatment genes/enzymes specifically adapted for use against agricultural feedstocks. Results: Metatranscriptomic profiling was performed on worker termite guts after feeding on corn stover (CS), soybean residue (SR), or 98% pure cellulose (paper) to identify (i) microbial community, (ii) pathway level and (iii) gene-level responses. Microbial community profiles after CS and SR feeding were different from the paper feeding profile, and protist symbiont abundance decreased significantly in termites feeding on SR and CS relative to paper. Functional profiles after CS feeding were similar to paper and SR; whereas paper and SR showed different profiles. Amino acid and carbohydrate metabolism pathways were downregulated in termites feeding on SR relative to paper and CS. Gene expression analyses showed more significant down regulation of genes after SR feeding relative to paper and CS. Stereotypical lignocellulase genes/enzymes were not differentially expressed, but rather were among the most abundant/constitutively-expressed genes. Conclusions: These results suggest that the effect of CS and SR feeding on termite gut lignocellulase composition is minimal and thus, the most abundantly expressed enzymes appear to encode the best candidate catalysts for use in saccharification of these and related second-generation feedstocks. Further, based on these findings we hypothesize that the most abundantly expressed lignocellulases, rather than those that are differentially expressed have the best potential as pretreatment enzymes for CS and SR feedstocks. © 2015 Rajarapu et al

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

The M Dwarf GJ 436 and its Neptune-Mass Planet

We determine stellar parameters for the M dwarf GJ 436 that hosts a Neptune-mass planet. We employ primarily spectral modeling at low and high resolution, examining the agreement between model and observed optical spectra of five comparison stars of type, M0-M3. Modeling high resolution optical spectra suffers from uncertainties in TiO transitions, affecting the predicted strengths of both atomic and molecular lines in M dwarfs. The determination of Teff, gravity, and metallicity from optical spectra remains at ~10%. As molecules provide opacity both in lines and as an effective continuum, determing molecular transition parameters remains a challenge facing models such as the PHOENIX series, best verified with high resolution and spectrophotometric spectra. Our analysis of GJ 436 yields an effective temperature of Teff = 3350 +/- 300 K and a mass of 0.44 Msun. New Doppler measurements for GJ 436 with a precision of 3 m/s taken during 6 years improve the Keplerian model of the planet, giving a minimum mass, M sin i = 0.0713 Mjup = 22.6 Mearth, period, P = 2.6439 d, and e = 0.16 +/- 0.02. The noncircular orbit contrasts with the tidally circularized orbits of all close-in exoplanets, implying either ongoing pumping of eccentricity by a more distant companion, or a higher Q value for this low-mass planet. The velocities indeed reveal a long term trend, indicating a possible distant companion.Comment: 27 pages, 7 figures, accepted to PAS

Unified View of Scaling Laws for River Networks

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added

Topological self-similarity on the random binary-tree model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented