302 research outputs found
Species assembly in model ecosystems, II: Results of the assembly process
In the companion paper of this set (Capitan and Cuesta, 2010) we have
developed a full analytical treatment of the model of species assembly
introduced in Capitan et al. (2009). This model is based on the construction of
an assembly graph containing all viable configurations of the community, and
the definition of a Markov chain whose transitions are the transformations of
communities by new species invasions. In the present paper we provide an
exhaustive numerical analysis of the model, describing the average time to the
recurrent state, the statistics of avalanches, and the dependence of the
results on the amount of available resource. Our results are based on the fact
that the Markov chain provides an asymptotic probability distribution for the
recurrent states, which can be used to obtain averages of observables as well
as the time variation of these magnitudes during succession, in an exact
manner. Since the absorption times into the recurrent set are found to be
comparable to the size of the system, the end state is quickly reached (in
units of the invasion time). Thus, the final ecosystem can be regarded as a
fluctuating complex system where species are continually replaced by newcomers
without ever leaving the set of recurrent patterns. The assembly graph is
dominated by pathways in which most invasions are accepted, triggering small
extinction avalanches. Through the assembly process, communities become less
resilient (e.g., have a higher return time to equilibrium) but become more
robust in terms of resistance against new invasions.Comment: 14 pages, 13 figures. Revised versio
Controlling the risky fraction process with an ergodic criterion
This article examines a tracking problem, similar to the one presented in Pliska and Suzuki (Quantitative Finance, 2004): an investor would keep constant proportions of her wealth in different assets if markets were frictionless; however, in the presence of fixed and proportional transaction costs her implementation problem is to keep asset proportions close to the target levels whilst avoiding too much intervention costs. Instead of minimizing discounted tracking error plus transaction costs over an infinite horizon, the optimization objective here is minimization of long run tracking error plus intervention costs per unit time. This ergodic problem is treated via combining basic tools from diffusion theory and nonlinear optimization techniques. A comparative sensitivity analysis of the ergodic and discounted problems is undertaken.
Stochastic impulse control with discounted and ergodic optimization criteria: A comparative study for the control of risky holdings
We consider a single-asset investment fund that in the absence of transactions costs would hold a constant amount of wealth in the risky asset. In the presence of market frictions wealth is allowed to fluctuate within a control band: Its upper (lower) boundary is chosen so that gains (losses) from adjustments to the target minus (plus) fixed plus proportional transaction costs maximize (minimize) a power utility function. We compare stochastic impulse control policies derived via ergodic and discounted optimization criteria. For the solution of the ergodic problem we use basic tools from the theory of diffusions whereas the discounted problem is solved after being characterized as a system of quasi-variational inequalities. For both versions of the problem, derivation of the control bands pertains to the numerical solution of a system of nonlinear equations. We solve numerous such systems and present an extensive comparative sensitivity analysis with respect to the parameters that characterize investor’s preferences and market behavior.Transaction costs; stochastic impulse control; ergodic criteria
AN OPTION VALUE APPROACH TO VALUING PRESERVATION PROPERTIES
There has been a recent trend towards purchasing land for farmland preservation, wildlife refuges, other conservation, and cultural and historical preservation. There is a great deal of unexplained variation in the dollars paid per acre for these properties. The theoretical basis for this analysis is an option value model with stochastic returns to development. The data used in our analysis is sales transactions data for natural resource conservation and farmland preservation purposes from throughout the United States. We find that land, when it would be best used for development, but is not developed, has a significantly higher price.Land Economics/Use,
An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm
Many physical and biological processes are stochastic in nature.
Computational models and simulations of such processes are a mathematical and
computational challenge. The basic stochastic simulation algorithm was
published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys.
Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make
the algorithm more efficient in terms of running time. All accelerated versions
of the algorithm are aimed at minimizing the running time required to produce a
stochastic trajectory in state space. In these simulations, a necessary
condition for reliable statistics is averaging over a large number of
simulations. In this study I present a new accelerating approach which does not
alter the stochastic algorithm, but reduces the number of required runs. By
analysis of collected data I demonstrate high precision levels with fewer
simulations. Moreover, the suggested approach provides a good estimation of
statistical error, which may serve as a tool for determining the number of
required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19
pages, including 2 Tables and 4 Figure
Aging in the random energy model
In this letter we announce rigorous results on the phenomenon of aging in the
Glauber dynamics of the random energy model and their relation to Bouchaud's
'REM-like' trap model. We show that, below the critical temperature, if we
consider a time-scale that diverges with the system size in such a way that
equilibrium is almost, but not quite reached on that scale, a suitably defined
autocorrelation function has the same asymptotic behaviour than its analog in
the trap model.Comment: 4pp, P
Subsidization of the Biofuel Industry: Security vs. Clean Air?
Replaced with revised version of paper 07/11/06.Resource /Energy Economics and Policy,
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