Martingale Option Pricing

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove it for much a much larger class of returns models where the diffusion coefficient depends on both returns x and time t. That option prices blow up if fat tails in logarithmic returns x are included in the market dynamics is also explained

Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets

Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade have reported that they arenon-Gaussian, scale in time, and have power-law(or fat) tails. However, because they use sliding interval methods of analysis, these studies implicitly assume that the underlying process has stationary increments. We explicitly show that this assumption is not valid for the Euro-Dollar exchange rate between 1999-2004. In addition, we find that fluctuations in returns of the exchange rate are uncorrelated and scale as power-laws for certain time intervals during each day. This behavior is consistent with a diffusive process with a diffusion coefficient that depends both on the time and the price change. Within scaling regions, we find that sliding interval methods can generate fat-tailed distributions as an artifact, and that the type of scaling reported in many previous studies does not exist.Comment: 12 pages, 4 figure

New set of measures to analyze non-equilibrium structures

We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface deposition. Patterns growth in the Cahn-Hilliard Equation (used to model spinodal decomposition) are shown to exhibit three distinct stages. Two models of surface growth, namely the continuous Kardar-Parisi-Zhang (KPZ) model and the discrete Restricted-Solid-On-Solid (RSOS) model are shown to have different saturation exponents

Monitoring Growth Performance of Naturally Regenerated Woody Species in an Enriched Pine Stand, Sri Lanka

Monitoring growth performance of newly recruited plant species after applying several silvicultural treatments in monoculture plantations is important to evaluate the success of forest restoration. This study was conducted in 2015 to determine the growth performance of the naturally regenerated woody plant species in an unrestored (UP) and a restored (RP) Pinus caribaea Morelet plantation, in lower Hantana, Sri Lanka. In RP, partial thinning of pines followed by enrichment planting of four broad-leaved tree species in 2003 and total thinning of pines was initiated in 2009. In both sites fifteen plots (5x5m) and within each of them three subplots (1x1m) were demarcated randomly. The height of seedlings (SE, <50 cm in height) in subplots and height of saplings (SA1= 50-129 and SA2=130-300 cm in height) and trees (TR, >300 cm in height) and dbh of SA2 and TR in all the plots were recorded. Collectively, 417 individuals (RP=298, UP=119) representing 28 species (RP=24, UP=12) and 22 plant families (RP=18, UP=13) survived by the end of the six months. The mean monthly increment of height (MMIH)of survived species in RP was higher for all the life forms except for SE (SE=1.35, SA1=1.61, SA2= 1.38, TR= 4.45 cmmo-1) than in UP (SE=2.06, SA1= 0.17, SA2= 0.00, TR= 1.65 cmmo-1). The MMIH of trees was significantly higher in RP than UP. The mean monthly increment of dbh (MMID) of survived individuals in RP was higher for both SA2 (0.017 cm per mo-1) and TR (0.027 cm per mo-1) than in UP (SA2= 0.0007, TR= 0.024 cmmo-1). The MMID of SA2 was significantly higher in RP than UP Of the 24 species tested in all four life form categories in RP, 19 (SE=39%, SA1=56%, SA2=69%, TR=85% of the species)had MMIH exceeding 1 cm mo-1while eight (SA2=5%, TR=26%) had dbh increment exceeding 0.05 cm mo-1. In UP, only five species (SE=60%, SA1=100%, SA2=25%, TR=77%of the species) had MMIH exceeding 1cm while one species (Alstonia macrophylla)(SA2=25%, TR=22%) had MMID exceeding0.05 cm mo-1. As the growth performance of the naturally regenerated woody species in RP was higher than UP, we conclude that restoration of pine plantation in mountainous regions of Sri Lanka, using silvicultural techniques is successful in achieving restoration goals.Keywords: Growth performance, Natural regeneration, Pinus plantation, Restoratio