In this survey, a short introduction in the recent discovery of log-normally distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data…
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48 results for “log-normal approach”
Entropy corrected geometric Brownian motionphysics.data-an
Entropy corrections improve GBM's predictive accuracy for non-log-normal distributions.
problem Log-normal distribution limitations in GBM predictions.
method Entropy corrections to geometric Brownian motion (GBM).
result Improved predictive accuracy for non-log-normal distributions.
Alternative closed-form formula for spread call option prices under log-normal models.
problem Valuation of spread call options under log-normal models.
method Developed an alternative closed-form formula for spread call option prices.
result Our formula performs better for certain range of model parameters than existing closed-form formula.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
problem Improving prediction of default portfolios using complex models.
method Applying Merton model with log-normal intensity function to Poisson process, discussing temporal correlation effects.
result Power decay model provides better generalization for long-term default portfolio data.
New approximations for Asian basket spread options using stochastic Taylor expansions.
problem Pricing Asian basket spread options under the Black-Scholes model.
method Stochastic Taylor expansion applied to a log-normal proxy model.
result Highly accurate approximations for Asian and spread options, without numerical integration.
Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits gro…
Quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian representation, which greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small…
In the LIBOR market model, forward interest rates are log-normal under their respective forward measures. This note shows that their distributions under the other forward measures of the tenor structure have approximately log-normal tails.
Gradually Truncated Log-normal distribution - Size distribution of firmscond-mat.stat-mech
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
Study on the geometric Dyson Brownian motion of non-square matrix products.
problem Understanding the spectrum of a product of non-square random matrices.
method Proportional depth-width limit followed by mean-field limit, solving Burgers equation.
result Free log-normal law is obtained in the identity-start case.
Pricing basket options with the first three moments of the basket: log-normal models and beyondq-fin.PR
Paper improves basket option pricing for log-normal models.
problem Challenges in pricing basket options with negative weights.
method Moment matching and solving a unary cubic equation.
result Highly accurate closed form solution for basket options.
This work introduces a geometric approach to probability representation and option pricing.
problem Representing probability distributions geometrically for better understanding and approximation.
method Introducing a geometric representation of probability using implied volatility and geometric transformations.
result Any probability distribution on positive reals can be represented by a planar curve, facilitating approximation and analysis.
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
Quasistatically varying log-normal distribution in the middle scale region of Japanese land pricesq-fin.ST
Employing data on the assessed value of land in 1974--2007 Japan, we exhibit a quasistatically varying log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed quasi-balance is adopted together with two approximations. The resultant distribution is power-law with the …
Paper characterizes DLN distribution, its properties, and estimation methods.
problem No specific problem stated, focuses on DLN distribution properties.
method Characterization of PDF, CDF, moments; generalization to N-dimensions; methods to handle double-exponential nature.
result Characterization of DLN distribution and its properties, including estimation methods.
Onflow optimizes portfolio allocation with gradient flows, robust to transaction fees.
problem Optimizing portfolio allocation with transaction costs.
method Gradient flow reinforcement learning method for dynamic asset allocation.
result Onflow outperforms benchmarks in high transaction cost regimes.
We propose a novel time discretization for the log-normal SABR model and derive its asymptotic properties.
problem Analyzing the log-normal SABR model's time-discretized behavior and implied volatility surface.
method We use the Euler-Maruyama scheme for time discretization and derive asymptotic properties in the limit of large number of time steps.
result We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in the asymptotic regime.
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior turns out to depend on the correlation between the components, and the explicit s…
A study of the personal income distribution in Australiaphysics.soc-ph
We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The lo…
Finite Mixtures of Multivariate Poisson-Log Normal Factor Analyzers for Clustering Count Datastat.ME
Flexible models cluster RNA sequencing data.
problem Clustering discrete data from RNA sequencing studies.
method Finite mixtures of multivariate Poisson-log normal factor analyzers with constraints.
result Models give favorable clustering performance on real and simulated data.
Bayesian model predicts oncology demand trends with high accuracy.
problem Accurate forecasting of oncology demand for resource planning.
method Boosting-based Bayesian conjugate models for Poisson process.
result Model outperforms other methods in trend detection accuracy.
3D dust map of the Milky Way improves resolution and accuracy.
problem Reconstructing the 3D dust distribution in the Milky Way.
method Gaussian process regression on spherical coordinates with iterative grid refinement.
result Improved 3D dust map with increased resolution and accuracy.
In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any …
The sum of log-normal variates in geometric Brownian motioncond-mat.stat-mech
Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology to economics. Trajectories of GBM are distributed according to the we…
RL and DTSOC for final quadratic hedging performance studied.
problem Optimal hedging of European call options with and without transaction costs.
method Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control.
result RL and DTSOC perform similarly to variance-optimal hedging in various market models.
Paper proposes a new reserving model using machine learning techniques.
problem Managing uncertainties in premium sufficiency and reserves for future claims.
method Stacked model combining Gradient Boosting, Random Forest, Artificial Neural Networks, and log-normal approach.
result The proposed model improves traditional reserving techniques, leading to more accurate reserving risk assessment.
Ordinal Regression with Fenton-Wilkinson Order Statistics: A Case Study of an Orienteering Racestat.AP
A new model predicts race places using changeover-times and log-normal distributions.
problem Predicting race places in orienteering races.
method Fenton-Wilkinson Order Statistics model based on log-normal leg-times and changeover-times.
result The model accurately predicts race places with smaller root-mean-square-errors.
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of …
Physicists' approach to studying socio-economic inequalities: Can humans be modelled as atoms?q-fin.GN
A brief overview of the models and data analyses of income, wealth, consumption distributions by the physicists, are presented here. It has been found empirically that the distributions of income and wealth possess fairly robust features, like the bulk of both the income and wealth distributions seem to reasonably fit …
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
Study shows big winner stocks significantly impact passive and active investment strategies.
problem Impact of big winner stocks on passive and active investment strategies.
method Numerical and analytical techniques applied to historical stock price data.
result Concentrated portfolios underperform equally weighted indexes due to missing big winner stocks.
Derives TAP approximation for Bayesian linear regression.
problem Log-normalizing constant of posterior distribution in high-dimensional linear regression.
method Variational representation and Thouless-Anderson-Palmer approximation.
result Proves TAP approximation for spherical prior in proportional asymptotic regime.
The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Completion have become popular methods for Link Prediction due to the low rank nature of mutual node fr…
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
Gaussian Recombining Split Treeq-fin.CP
A new tree model, GRST, improves option pricing without log-normality assumptions.
problem Limitations of CRR binomial trees in valuing securities with early exercise characteristics.
method Gaussian Recombining Split Tree (GRST) that generates a discrete probability mass function approximating a Gaussian distribution.
result Option prices from GRST align closely with market prices.
WENDy now estimates nonlinear ODEs with noisy data.
problem Estimating parameters of nonlinear ODEs with noisy data.
method WENDy-MLE algorithm for maximum likelihood estimation of nonlinear-in-parameters ODEs.
result WENDy-MLE outperforms other methods in accuracy, speed, and domain of convergence.
Tree-based variational inference improves PLN model for hierarchical count data.
problem Limited applicability of PLN model in ecosystems due to lack of hierarchical tree structures.
method Introduced PLN-Tree model integrating structured variational inference techniques.
result Enhanced generative improvements and practical interpretability in microbiome modeling.
Wealth Dynamics on Complex Networkscond-mat.dis-nn
We study a model of wealth dynamics [Bouchaud and Mézard 2000, \emph{Physica A} \textbf{282}, 536] which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network. The extreme cases of a fully connected and a ful…
Estimates returns for dollar cost averaging using geometric Brownian motion.
problem Estimating returns for dollar cost averaging investing strategy.
method Uses geometric Brownian motion and log-Normal distribution to construct a lower bound for returns. Computes parameters recursively and in closed form for dollar cost averaging. Compares to lump sum investing for matching wealth distributions.
result Probability of negative returns is less than 2.5% for 40 years of annual dollar cost averaging.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
Re-examination of the size distribution of firmsphysics.soc-ph
In this paper we address the question of the size distribution of firms. To this aim, we use the Bloomberg database comprising multinational firms within the years 1995-2003, and analyze the data of the sales and the total assets of the separate financial statement of the Japanese and the US companies, and make a compa…
Bayesian inference and superstatistics to describe long memory processes of financial time seriesq-fin.ST
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
problem Modeling correlated volatility in financial time series with heavy tails and long memory.
method Superstatistical dynamics, Bayesian Inference, Metropolis-Hasting sampling.
result The log-Normal model is reliable for short timescales, while inverse-Gamma is preferred for long timescales.
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distri…