A new process generalizes geometric Brownian motion with asymmetry.
problem Creating a positive process with asymmetry parameter.
method Introducing asymmetry parameter α to describe volatility at new lows.
result Preserves GBM properties while expressing volatility as weighted mean.
The paper studies discrete sums of geometric Brownian motions in finance.
problem Modeling stochastic annuities and pricing Asian options.
method Analyzes probability distributions and asymptotic behavior of discrete sums of geometric Brownian motions.
result Derives tail asymptotics and computes asymptotic distribution functions for discrete sums.
Solves optimal liquidation problem for stock price following geometric Brownian motion.
problem Optimal liquidation problem for stock price process following geometric Brownian motion.
method Functional analysis tools; working in terms of cash.
result Explicit solution to the problem, extending to stochastic drift.
New method calculates geometric Brownian motion with affine drift and its integral.
problem Calculating the distribution of geometric Brownian motion with affine drift and its integral.
method Laplace transform approach and Heun differential equation.
result Joint distribution of geometric Brownian motion with affine drift and its integral can be determined.
GMMNs model cross-sectional dependence for better option pricing and simulation.
problem Modeling cross-sectional dependence between stochastic processes.
method Generative moment matching networks (GMMNs) for geometric Brownian motions and ARMA-GARCH models.
result GMMNs produce dependent quasi-random samples with variance reduction.
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.
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.
The paper studies variable annuity benefits using exponential functionals of Levy processes.
problem Modeling equity returns with a Levy process to better fit market features.
method Uses exponential functionals of a Levy process to compute the distribution of variable annuity guaranteed benefits.
result Explicitly computes the distribution of certain exponential functionals.
Study optimal dividends in dual risk model with stochastic interest rate.
problem Optimal dividend strategy in dual risk model with stochastic interest rate.
method Geometric Brownian motion or exponential Lévy process for discounting factor.
result Closed form solutions can be obtained for optimal dividends.
Study optimizes financial market disclosure by analyzing withheld information.
problem Optimizing financial market disclosure in partially observed, privately held firms.
method Analyzes geometric-Brownian state processes with Poisson observation times, derives filtering formulas for withheld information.
result Explicit formulas for downgrading valuations in the absence of disclosures.
We extend Hawkes processes by treating self-excitation levels as stochastic processes.
problem Approximating events and intensities that accelerate each other in correlated contagion.
method Proposed an extension to Hawkes processes with stochastic excitation levels, generalized algorithm for simulation, and hybrid MCMC approach for model fitting.
result Our approach allows better approximation in domains where events and intensities accelerate each other.
Study of a generalized geometric Brownian motion with varying entry and exit rates.
problem Understanding the long-run behavior of economic systems with growth, volatility, entry, and exit.
method Generalized geometric Brownian motion framework with varying entry and exit rates, analyzing moments and survival probability.
result Optimal exit rate minimizes mean first-passage time, influencing system outcome.
In this paper, we consider the asset-liability management under the mean-variance criterion. The financial market consists of a risk-free bond and a stock whose price process is modeled by a geometric Brownian motion. The liability of the investor is uncontrollable and is modeled by another geometric Brownian motion. W…
Optimizes dividend payout in insurance wealth process with stochastic interest rate.
problem Maximizing expected discounted dividends up to ruin in insurance wealth process.
method Modelled compound Poisson process with stochastic interest rate, solved using HJB equation.
result Explicit expression for value function and optimal strategy in geometric Brownian motion case.
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.
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.
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.
New binomial model fits all moments to geometric Brownian motion.
problem Discontinuity problem in option pricing.
method Constructs a generalized binomial tree model.
result Resolves discontinuity problem in option pricing.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
Researchers calculate the Laplace transform of a geometric Brownian motion integral.
problem Calculating the Laplace transform of a specific integral functional of geometric Brownian motion.
method Analytical calculation of the Laplace transform of the cumulative distribution and probability density functions.
result The Laplace transform of the integral functional of geometric Brownian motion is derived.
The paper proposes estimators for bid-ask spreads with and without serial dependence.
problem Estimating bid-ask spreads in financial markets with and without serial dependence.
method The authors propose moment-based estimators for bid-ask spreads, considering both geometric Brownian motion and geometric fractional Brownian motion for price dynamics, and Ornstein-Uhlenbeck process for microstructure noise.
result The estimators are consistent and asymptotically normal, and perform well compared to existing approaches on simulated data.
The paper studies the discrete-time average of geometric Brownian motion and its application to Asian options pricing.
problem Understanding the pricing of Asian options with discrete-time averaging.
method Deriving asymptotics for the discrete-time average of geometric Brownian motion and analyzing its impact on Asian options pricing.
result Derives the asymptotics for the price of Asian options with discrete-time averaging in the Black-Scholes model.
Reflected geometric Brownian motion models are not arbitrage-free.
problem No-arbitrage condition violation in financial markets.
method Analysis of reflected geometric Brownian motion models.
result Models violate even the weakest no-arbitrage condition.
This paper studies the parabolic free boundary problem arising from pricing American-style put options on an asset whose index follows a geometric Brownian motion process. The contribution is to propose a condition for that the early exercise boundary is a convex function.
Paper compares stock price prediction models using Heston and Geometric Brownian Motion.
problem Predicting stock prices accurately.
method Developed Heston and Geometric Brownian Motion models using Ito's lemma and Euler-Maruyama methods.
result Models outperform statistical indicators in predicting stock prices.
Enhances binomial and trinomial models for equity options pricing.
problem Improving accuracy of equity option pricing models.
method Develops time-dependent binomial model and introduces a risk-neutral trinomial tree.
result Equates moments of pricing tree increments to geometric Brownian motion.
The evolution of prices on ideal market is given by geometrical Brownian motion, where Gaussian white noise describes fluctuations. We study the effect of correlations introduced by a color noise.
Study naive vs sophisticated agents stopping a diffusion process with time-inconsistent payoffs.
problem Time-inconsistent stopping problem for diffusion processes.
method Analyzes naive and sophisticated agents' strategies, proving equilibrium existence.
result Equilibrium strategies can be derived as fixed points of strategic reasoning operators.
Optimal portfolio tracking with dynamic capital injection into a ratcheting benchmark.
problem Optimizing a portfolio's performance by dynamically adding capital to a non-decreasing benchmark.
method Formulated as an unconstrained control problem with a running maximum cost, transformed into an auxiliary problem with a nonlinear HJB equation, solved using probabilistic representation and stochastic flow analysis.
result Established the existence of a unique classical solution to the HJB equation, providing feedback optimal portfolio strategies.
The paper extends Merton's problem by adding benchmark tracking, finding optimal strategies.
problem Maximizing consumption utility with a trade-off against benchmark performance.
method Developed a convex duality theorem and derived optimal strategies for specific cases.
result Found optimal portfolio and consumption strategies for CRRA utility and geometric Brownian motion benchmarks.
The paper models asset prices with random volatility to match option prices.
problem Matching asset price dynamics with observed option prices.
method Uses a mixture of diffusion processes with random volatility.
result Derives explicit pricing formulas for derivatives.
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
Optimizes trading in a market with a change point, considering risk and information constraints.
problem Maximizing utility in a financial market with a change point in parameters.
method Solves an optimization problem using martingale representation results for different filtrations.
result Calculates the utility indifference value for a specific utility function and risk measure.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
The paper examines short-term volatilities in equity indexes using a ranking procedure.
problem Understanding short-term behaviors of implied volatility in equity markets.
method Using a ranking procedure to model equity index dynamics, the paper investigates the short-term volatilities of derivatives written on indexes.
result The models reconcile the long memory of volatilities and power law of ATM skews in equity markets.
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
In this paper we derive the optimal execution trajectory for a trader who wishes to buy or sell a large position of shares which evolve as a geometric Brownian process in contrast to the arithmetic model which prevails in the existing literature, and with a general temporary impact h. We provide a couple of examples …
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 …
Paper offers a fast method to assess DeFi liquidation risk.
problem Assessing liquidation risk in DeFi stablecoin lending.
method Modeling collateral exchange rate as zero-drift geometric Brownian motion.
result Derives an exact formula for liquidation probability.
Modeling price dynamics in AMMs with fees using geometric Brownian motion.
problem Understanding price dynamics in AMMs with transaction fees.
method Geometric Brownian motion, local times, excursion theory.
result Derivation of time-changed representation and limiting behavior of AMM prices.
Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.
problem Modeling continuous martingales with prescribed initial and terminal distributions.
method Developed geometric Bass martingales and established their properties.
result Explicit bijection and representation of geometric Bass martingales.
Asymptotic Laplace transform for geometric Brownian motion applied to bond pricing.
problem Laplace transform of geometric Brownian motion time integral.
method Asymptotic analysis for σ2To0 limit. result Approximation for zero coupon bond prices in Dothan model.
Quantum algorithms for financial derivatives and credit risk.
problem Estimating credit risk and option pricing in realistic financial models.
method Developed a regime switching volatility model for financial markets, using a Markov chain to determine volatility parameters.
result Quantum algorithms can be applied to realistic financial models, bringing quantum computing closer to practical applications.
We derive the optimal investment decision in a project where both demand and investment costs are stochastic processes, eventually subject to shocks. We extend the approach used in Dixit and Pindyck (1994), chapter 6.5, to deal with two sources of uncertainty, but assuming that the underlying processes are no longer ge…
We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process. Optimal portfolios and maximum expected log--linear utilities from terminal wealth f…
In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal …
Optimizes pension fund management under funding risks.
problem Managing DB pension fund under underfunded and overfunded conditions.
method Stochastic model with Ornstein-Uhlenbeck interest rate, geometric Brownian motion for benefits, and cash, bond, stock investments.
result Optimal wealth process, portfolio, and efficient frontier obtained under various tolerance levels for solvency risk.
Study on efficiency of Dutch auctions on blockchains considering various parameters.
problem Efficiency and fairness in Dutch auctions on blockchains.
method Modeling Dutch auctions with Poisson process and geometric Brownian motion, computing expected losses and time-to-fill.
result Tradeoff between speed and quality in Dutch auctions, useful for setting parameters.