7,266 research outputs found
Optimal Investment in the Development of Oil and Gas Field
Let an oil and gas field consists of clusters in each of which an investor
can launch at most one project. During the implementation of a particular
project, all characteristics are known, including annual production volumes,
necessary investment volumes, and profit. The total amount of investments that
the investor spends on developing the field during the entire planning period
we know. It is required to determine which projects to implement in each
cluster so that, within the total amount of investments, the profit for the
entire planning period is maximum.
The problem under consideration is NP-hard. However, it is solved by dynamic
programming with pseudopolynomial time complexity. Nevertheless, in practice,
there are additional constraints that do not allow solving the problem with
acceptable accuracy at a reasonable time. Such restrictions, in particular, are
annual production volumes. In this paper, we considered only the upper
constraints that are dictated by the pipeline capacity. For the investment
optimization problem with such additional restrictions, we obtain qualitative
results, propose an approximate algorithm, and investigate its properties.
Based on the results of a numerical experiment, we conclude that the developed
algorithm builds a solution close (in terms of the objective function) to the
optimal one
Life, Death and Preferential Attachment
Scientific communities are characterized by strong stratification. The highly
skewed frequency distribution of citations of published scientific papers
suggests a relatively small number of active, cited papers embedded in a sea of
inactive and uncited papers. We propose an analytically soluble model which
allows for the death of nodes. This model provides an excellent description of
the citation distributions for live and dead papers in the SPIRES database.
Further, this model suggests a novel and general mechanism for the generation
of power law distributions in networks whenever the fraction of active nodes is
small.Comment: 5 pages, 2 figure
A dynamic and multifunctional account of middle‐range theories
This article develops a novel account of middle‐range theories for combining theoretical and empirical analysis in explanatory sociology. I first revisit Robert K. Merton’s original ideas on middle‐range theories and identify a tension between his developmental approach to middle‐range theorizing that recognizes multiple functions of theories in sociological research and his static definition of the concept of middle‐range theory that focuses only on empirical testing of theories. Drawing on Merton's ideas on theorizing and recent discussions on mechanism‐based explanations, I argue that this tension can be resolved by decomposing a middle‐range theory into three interrelated and evolving components that perform different functions in sociological research: (i) a conceptual framework about social phenomena that is a set of interrelated concepts that evolve in close connection with empirical analysis; (ii) a mechanism schema that is an abstract and incomplete description of a social mechanism; and (iii) a cluster of all mechanism‐based explanations of social phenomena that are based on the particular mechanism schema. I show how these components develop over time and how they serve different functions in sociological theorizing and research. Finally, I illustrate these ideas by discussing Merton’s theory of the Matthew effect in science and its more recent applications in sociology.This article develops a novel account of middle‐range theories for combining theoretical and empirical analysis in explanatory sociology. I first revisit Robert K. Merton’s original ideas on middle‐range theories and identify a tension between his developmental approach to middle‐range theorizing that recognizes multiple functions of theories in sociological research and his static definition of the concept of middle‐range theory that focuses only on empirical testing of theories. Drawing on Merton's ideas on theorizing and recent discussions on mechanism‐based explanations, I argue that this tension can be resolved by decomposing a middle‐range theory into three interrelated and evolving components that perform different functions in sociological research: (i) a conceptual framework about social phenomena that is a set of interrelated concepts that evolve in close connection with empirical analysis; (ii) a mechanism schema that is an abstract and incomplete description of a social mechanism; and (iii) a cluster of all mechanism‐based explanations of social phenomena that are based on the particular mechanism schema. I show how these components develop over time and how they serve different functions in sociological theorizing and research. Finally, I illustrate these ideas by discussing Merton’s theory of the Matthew effect in science and its more recent applications in sociology.Peer reviewe
Evolutionary estimation of a Coupled Markov Chain credit risk model
There exists a range of different models for estimating and simulating credit
risk transitions to optimally manage credit risk portfolios and products. In
this chapter we present a Coupled Markov Chain approach to model rating
transitions and thereby default probabilities of companies. As the likelihood
of the model turns out to be a non-convex function of the parameters to be
estimated, we apply heuristics to find the ML estimators. To this extent, we
outline the model and its likelihood function, and present both a Particle
Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm
to maximize the likelihood function. Numerical results are shown which suggest
a further application of evolutionary optimization techniques for credit risk
management
Interest Rates and Information Geometry
The space of probability distributions on a given sample space possesses
natural geometric properties. For example, in the case of a smooth parametric
family of probability distributions on the real line, the parameter space has a
Riemannian structure induced by the embedding of the family into the Hilbert
space of square-integrable functions, and is characterised by the Fisher-Rao
metric. In the nonparametric case the relevant geometry is determined by the
spherical distance function of Bhattacharyya. In the context of term structure
modelling, we show that minus the derivative of the discount function with
respect to the maturity date gives rise to a probability density. This follows
as a consequence of the positivity of interest rates. Therefore, by mapping the
density functions associated with a given family of term structures to Hilbert
space, the resulting metrical geometry can be used to analyse the relationship
of yield curves to one another. We show that the general arbitrage-free yield
curve dynamics can be represented as a process taking values in the convex
space of smooth density functions on the positive real line. It follows that
the theory of interest rate dynamics can be represented by a class of processes
in Hilbert space. We also derive the dynamics for the central moments
associated with the distribution determined by the yield curve.Comment: 20 pages, 3 figure
An Optimal Execution Problem with Market Impact
We study an optimal execution problem in a continuous-time market model that
considers market impact. We formulate the problem as a stochastic control
problem and investigate properties of the corresponding value function. We find
that right-continuity at the time origin is associated with the strength of
market impact for large sales, otherwise the value function is continuous.
Moreover, we show the semi-group property (Bellman principle) and characterise
the value function as a viscosity solution of the corresponding
Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of
the optimal strategies change completely, depending on the amount of the
trader's security holdings and where optimal strategies in the Black-Scholes
type market with nonlinear market impact are not block liquidation but gradual
liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal
execution problem with market impact" in Finance and Stochastics (2014
The mathematical review system: does reviewer status play a role in the citation process?
This paper revisits an aspect of citation theory (i.e., citer motivation) with respect to the Mathematical Review system and the reviewer’s role in mathematics. We focus on a set of journal articles (369) published in Singularity Theory (1974–2003), the mathematicians who wrote editorial reviews for these articles, and the number of citations each reviewed article received within a 5 year period. Our research hypothesis is that the cognitive authority of a high status reviewer plays a positive role in how well a new article is received and cited by others. Bibliometric evidence points to the contrary: Singularity Theorists of lower status (junior researchers) have reviewed slightly more well-cited articles (2–5 citations, excluding author self-citations) than their higher status counterparts (senior researchers). One explanation for this result is that lower status researchers may have been asked to review ‘trendy’ or more accessible parts of mathematics, which are easier to use and cite. We offer further explanations and discuss a number of implications for a theory of citation in mathematics. This research opens the door for comparisons to other editorial review systems, such as book reviews written in the social sciences or humanities
Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model
Path integral techniques for the pricing of financial options are mostly
based on models that can be recast in terms of a Fokker-Planck differential
equation and that, consequently, neglect jumps and only describe drift and
diffusion. We present a method to adapt formulas for both the path-integral
propagators and the option prices themselves, so that jump processes are taken
into account in conjunction with the usual drift and diffusion terms. In
particular, we focus on stochastic volatility models, such as the exponential
Vasicek model, and extend the pricing formulas and propagator of this model to
incorporate jump diffusion with a given jump size distribution. This model is
of importance to include non-Gaussian fluctuations beyond the Black-Scholes
model, and moreover yields a lognormal distribution of the volatilities, in
agreement with results from superstatistical analysis. The results obtained in
the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl
Eroding market stability by proliferation of financial instruments
We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the
development of financial instruments, with a dynamical picture of an
interacting market, in a simple setting. The proliferation of financial
instruments apparently provides more means for risk diversification, making the
market more efficient and complete. In the simple market of interacting traders
discussed here, the proliferation of financial instruments erodes systemic
stability and it drives the market to a critical state characterized by large
susceptibility, strong fluctuations and enhanced correlations among risks. This
suggests that the hypothesis of APT may not be compatible with a stable market
dynamics. In this perspective, market stability acquires the properties of a
common good, which suggests that appropriate measures should be introduced in
derivative markets, to preserve stability.Comment: 26 pages, 8 figure
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