165,547 research outputs found
On Segre's Lemma of Tangents
Segre's lemma of tangents dates back to the 1950's when he used it in the proof
of his "arc is a conic" theorem. Since then it has been used as a tool to prove
results about various objects including internal nuclei, Kakeya sets, sets with few
odd secants and further results on arcs. Here, we survey some of these results
and report on how re-formulations of Segre's lemma of tangents are leading to new
results
A Complete Market Model for Option Valuation
This paper is an introduction and survey of Black-Scholes Model as a complete model for Option Valuation. It is a Stochastic processes that represent diffusive dynamics, a common and improved modelling assumption for financial systems. As the markets are frictionless generally, it becomes very necessary for us to use a more convenient and complete method in order to avoid errors for computations. We include a review of Stochastic Differential equations(SDE), the -lemma which gives a clear picture of Log-normal distribution of a Geometrical Brownian Motion path and solution of Black- Scholes Model Keywords: Stochastic Differential Equations, ’s lemma, tame and completeness of Black-Scholes Mode
Eigenvectors of random matrices: A survey
Eigenvectors of large matrices (and graphs) play an essential role in
combinatorics and theoretical computer science. The goal of this survey is to
provide an up-to-date account on properties of eigenvectors when the matrix (or
graph) is random.Comment: 64 pages, 1 figure; added Section 7 on localized eigenvector
Survey on the geometric Bogomolov conjecture
This is a survey paper of the developments on the geometric Bogomolov
conjecture. We explain the recent results by the author as well as previous
works concerning the conjecture. This paper also includes an introduction to
the height theory over function fields and a quick review on basic notions on
non-archimedean analytic geometry.Comment: 57 pages. This is an expanded lecture note of a talk at
"Non-archimedean analytic Geometry: Theory and Practice" (24--28 August,
2015). It has been submitted to the conference proceedings. Appendix adde
Optimal Data Acquisition for Statistical Estimation
We consider a data analyst's problem of purchasing data from strategic agents
to compute an unbiased estimate of a statistic of interest. Agents incur
private costs to reveal their data and the costs can be arbitrarily correlated
with their data. Once revealed, data are verifiable. This paper focuses on
linear unbiased estimators. We design an individually rational and incentive
compatible mechanism that optimizes the worst-case mean-squared error of the
estimation, where the worst-case is over the unknown correlation between costs
and data, subject to a budget constraint in expectation. We characterize the
form of the optimal mechanism in closed-form. We further extend our results to
acquiring data for estimating a parameter in regression analysis, where private
costs can correlate with the values of the dependent variable but not with the
values of the independent variables
Empirical likelihood confidence intervals for complex sampling designs
We define an empirical likelihood approach which gives consistent design-based confidence intervals which can be calculated without the need of variance estimates, design effects, resampling, joint inclusion probabilities and linearization, even when the point estimator is not linear. It can be used to construct confidence intervals for a large class of sampling designs and estimators which are solutions of estimating equations. It can be used for means, regressions coefficients, quantiles, totals or counts even when the population size is unknown. It can be used with large sampling fractions and naturally includes calibration constraints. It can be viewed as an extension of the empirical likelihood approach to complex survey data. This approach is computationally simpler than the pseudoempirical likelihood and the bootstrap approaches. The simulation study shows that the confidence interval proposed may give better coverages than the confidence intervals based on linearization, bootstrap and pseudoempirical likelihood. Our simulation study shows that, under complex sampling designs, standard confidence intervals based on normality may have poor coverages, because point estimators may not follow a normal sampling distribution and their variance estimators may be biased.<br/
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