Developed a new statistic to test binary regime switching models.
problem Testing the model assumption of binary regime switching extension of GBM.
method Proposed a new discriminating statistics and identified an admissible class of regime switching candidate models.
result Sampling distribution of the test statistics differs significantly between different regime switching models.
Optimal futures trading strategy in a changing market model.
problem Dynamic trading in a regime-switching market.
method Utility maximization approach with HJB equations reduced to linear ODEs.
result Optimal futures positions and portfolio value across market regimes.
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a…
The study extends GBM to include stable nonzero prices and finds a pronounced potential well.
problem The standard GBM model cannot describe stable nonzero prices in financial dynamics.
method Generalized GBM with polynomial drift of order q, model selection, and Markov chain Monte Carlo ensembles of potential functions.
result The optimal model for financial data is q=2, indicating the existence of a stable price.
Study models illiquid stock prices and finds low correlation due to constant prices.
problem Modeling illiquid stock prices and measuring correlation accurately.
method Combined Markov model with Ornstein Uhlenbeck and geometric Brownian motion.
result Low correlation in USE stocks due to constant prices and illiquidity.
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.
In this paper we propose a semi-Markov modulated model of interest rates. We assume that the switching process is a semi-Markov process with finite state space E and the modulated process is a diffusive process. We derive recursive equations for the higher order moments of the discount factor and we describe a Monte Ca…
Researchers develop a generalised geometric Brownian motion for better asset pricing.
problem Irregularities in simple geometric Brownian motion for asset dynamics.
method Introduce a memory kernel to generalise GBM, derive moments and probability density functions.
result The performance of kernels in pricing options depends on option maturity and moneyness.
Bayesian GBMs improve predictive uncertainty calibration for tabular data.
problem Lack of well-calibrated predictive uncertainties in gradient boosting machines.
method Variational inference with soft decision trees.
result Variational soft GBMs provide useful uncertainty estimates and maintain good predictive performance.
Paper proposes a new financial fraud detection system using improved RF and GBM.
problem Detecting financial fraud with high accuracy and efficiency.
method Introduces GBM-SSRF, a novel model combining GBM and SSRF.
result GBM-SSRF model outperforms traditional methods in fraud detection.
AGBM accelerates GBM with theoretical guarantees.
problem Accumulation of errors in GBM's momentum term.
method Incorporates Nesterov's acceleration techniques and a corrected pseudo residual.
result First GBM type with theoretically-justified accelerated convergence rate.
We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for existence of optimal policies and find closed-form expressions for the optimal v…
Study of Markov-modulated affine processes for richer models in finance.
problem Richer models in various applications.
method Martingale problem approach, characteristic function derivation, mathematical properties study.
result Existence and characteristic function of Markov-modulated affine processes.
Exact solutions found for a new SV model with stationary volatility.
problem Finding exact solutions for a new SV model.
method Analytical solutions for transition probability density, option values, and martingale defect.
result First example of an SV model with exact solutions, GBM volatility, and stationary volatility.
GBM outperforms DL in credit scoring tasks, but performance depends on dataset.
problem Benchmarking deep learning vs. gradient boosting for credit scoring.
method Used three datasets with different features to compare DL and GBM.
result GBM is more powerful and faster than DL for credit scoring.
New method corrects bias in feature importance measures of GBM.
problem Bias in feature importance measures of GBM.
method Cross-validated unbiased base learners.
result Significant improvement in feature importance measures with minimal computational cost.
Enhances count process modelling with Markov-modulated non-homogeneous Poisson process.
problem Count data modelling challenges, especially in complex scenarios.
method Introduces a flexible frequency perturbation measure into Markov-modulated Poisson process framework.
result Natural incorporation of observed event arrivals and latent factors.
This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Marko…
RGBM improves GBM efficiency with randomization.
problem Limited theoretical understanding of Gradient Boosting Machine.
method Randomization scheme to reduce search in weak-learners space.
result RGBM leads to substantial computational gains compared to GBM.
Study finds GBM model accurately predicts stock prices on Ghana Stock Exchange.
problem Investigating the suitability of GBM for modeling stock price dynamics.
method Geometric Brownian Motion model applied to weekly and monthly returns of equities listed on the Ghana Stock Exchange.
result GBM model accurately forecasts stock prices with minimal deviations, as evidenced by MSE evaluations.
Proposes MLEs for MMJDM with EM-algorithm.
problem Estimating stock prices with varying drift and volatility.
method EM-algorithm for MLEs of MMJDM.
result Validated with simulated data and fitted to Amazon and Netflix stock prices.
A method interprets black-box models using an ensemble of gradient boosting machines.
problem Local and global interpretation of black-box models.
method An ensemble of gradient boosting machines (GBMs) to form a generalized additive model.
result Efficiency and properties demonstrated on synthetic and real datasets.
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…
A new ensemble model uses simple hyper-rectangles to improve gradient boosting machine performance.
problem Improving gradient boosting machine performance and avoiding overfitting.
method Proposes a new ensemble model with axis-parallel hyper-rectangles as base models, integrates into GBM, and uses SHAP for interpretation.
result GBM with HRBMs can be an effective and interpretable model for regression and classification problems.
Study benchmarks cryptocurrency risk using GBM, revealing Lognormal limitations.
problem Tackles limitations of Lognormal assumption in modeling cryptocurrency volatility and VaR.
method Applies Geometric Brownian Motion (GBM) with Maximum Likelihood Estimation and correlated Monte Carlo Simulation.
result Observed limitations of Lognormal assumption in cryptocurrency volatility and VaR calculations.
This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models have been well-documented. This project extends that notion to a c…
AGBoost uses attention weights to improve GBM for regression problems.
problem Improving gradient boosting machine for regression tasks.
method Attention-based modification of GBM with trainable attention weights.
result AGBoost achieves better performance on regression datasets.
The Open University studies student online behavior in virtual learning environments.
problem Improving retention rates in online modules.
method GUHA and Markov chain-based analysis of student activity.
result Both methods are valid for modeling student activities.
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…
Study long-term behavior of semi-Markov modulated processes using integral functions.
problem Analyzing long-term behavior of semi-Markov modulated processes involving integral functions.
method Using ergodic semi-Markovian environment and affine stochastic recurrence equation.
result Mixture type laws emerge in long-term limit for processes.
Model detects market anomalies using a Hawkes process with hidden Markov chain.
problem Detecting high-frequency market manipulation in cryptocurrency trades.
method Developed a Markov-modulated Hawkes process with piecewise constant excitation kernels.
result Demonstrated the model's effectiveness in detecting suspicious trading activities.
This paper compares LSM and ANN/GBM for pricing American put options under a complex model.
problem Pricing American put options using advanced techniques.
method Least-Squares Monte Carlo (LSM) and Artificial Neural Network (ANN) and Gradient Boosted Machine (GBM) Trees.
result LSM outperforms ANN and GBM in pricing American put options.
Transfer learning improves activity recognition accuracy on smartwatches.
problem Inconsistent activity recognition accuracy across different users.
method On-device calibration of GBM by tuning parameters without retraining.
result Significant improvement in user-based accuracy for activity recognition.
We solve a broad class of sequential decision-making problems with partially observed states.
problem Sequential decision-making under uncertainty with partially observed states.
method Modeling as a partially observed Markov decision process (POMDP) and separating state and modulation process.
result The approach allows for specialized approximate solution procedures.
Improved contact tracing models outperform NIST challenge results.
problem Contact tracing using phone data and machine learning.
method Developed two machine learning models (GBM and MLP) from phone instrumental data features.
result Outperformed the leading NIST challenge result by HKUST.
Automated model tracks mouse behavior in home cages.
problem Confounding analysis in specialized arenas.
method Group Behaviour Model (GBM) using permutation matrix.
result Model captures individual and group behavior.
New models optimize quotes for automated market makers considering various price dynamics and demand variability.
problem Optimizing quotes for automated market makers in volatile price environments.
method Advanced models incorporating stochastic volatility, jumps, Hawkes processes, and Markov-modulated Poisson processes.
result Optimal quotes can be computed using numerical methods tailored to each model.
The paper proposes pricing methods for multi-asset generalized variance swaps.
problem Hedging risk in financial markets with complex asset structures.
method Proposes pricing methods for two new measures of generalized variance (maximum eigen-value and trace of covariance matrix) under Markov-modulated volatilities.
result Demonstrates pricing results for three stocks, highlighting the usefulness of these swaps in commodity risk management.
HypeGBMS clusters data in hyperbolic space, overcoming Euclidean limitations.
problem Clustering in hierarchical or tree-like datasets in curved spaces.
method Hyperbolic Gaussian Blurring Mean Shift with Möbius-weighted means.
result HypeGBMS effectively captures latent hierarchies in non-Euclidean data.
The study revisits portfolio diversification by relaxing assumptions for skewed, multi-regime, and leptokurtic asset returns.
problem Underestimation of risk in portfolio diversification due to assumptions that are inconsistent with real-world asset returns.
method Calibrated a Markov-modulated Levy process model to equity market data to demonstrate the merits of the approach.
result The calibrated models effectively match empirical moments and show the importance of relaxing assumptions in portfolio diversification.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
problem Effects of stochastic resetting on geometric Brownian motion.
method Analysis of geometric Brownian motion under stochastic resetting.
result Resetting makes geometric Brownian motion stationary but non-ergodic.
Optimal trading strategy with unobservable pricing errors for co-integrated assets.
problem Dynamic portfolio optimization of convergence trading with unobservable pricing errors.
method Modeling of convergence trading strategy with unobservable Markov-modulated pricing errors, extending Liu and Timmermann (2013) model.
result Characterization of optimal portfolio strategies in full and partial information settings.
Optimal dividend strategy found for risk models with regime switching.
problem Optimal dividend strategy for spectrally negative Markov additive models with regime switching.
method Introduced an auxiliary problem and transformed the original problem into a local optimization problem.
result The refraction-reflection strategy with regime-modulated thresholds is optimal.
We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this fil…
Study shows physical drift affects put-call parity enforcement, not just option payoffs.
problem Inconsistency between quoted put-call parity and actual market behavior.
method Examined SPX and RUT index options, used drift-preserving GBM term to improve fit.
result Physical drift enters the enforcement of risk-neutral parity, not just option payoffs.
Model explains asset price dynamics, defaults, and market crashes via non-linear dynamics.
problem Understanding asset price dynamics, defaults, and market crashes in financial markets.
method Proposes a non-equilibrium model incorporating market frictions and feedback mechanisms.
result The QED model produces non-linear dynamics, broken scale invariance, and corporate defaults.
We consider a limit order book, where buyers and sellers register to trade a security at specific prices. The largest price buyers on the book are willing to offer is called the market bid price, and the smallest price sellers on the book are willing to accept is called the market ask price. Market ask price is always …
This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states of the economy described…