arXiv research

The FSRM uses a multifractional process to capture price multifractality, revealing serial information for forecasting.

Study approximates rough stochastic volatility models using diffusion processes.

Approximates derivative pricing under fractional stochastic volatility.

New neural operators model turbulence with memory and randomness.

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

New IBP formulae for rough stochastic Volterra processes.

Study large deviations in fractional volatility models with non-Gaussian volatility.

New framework for ranking distributions using variable fractional parameters.

Modeling financial markets with memory using fractional calculus and Brownian motion.

In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- tions, for a hyperregular Lagrange function. From the stochastic fr…

New model uses generalized fractional Brownian motion for stock price prediction.

New rough stochastic volatility models using log-modulated fractional Brownian motion.

Uniform small energy regularity for fractional geometric problems proved.

Proposes new rule for ranking investment prospects over long horizons.

The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot…

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…

The paper models cryptocurrency price and volatility with jumps and fractional volatility.

Study shows how certain stochastic models reach a steady state over time.

We describe a graph-based semi-supervised learning framework in the context of deep neural networks that uses a graph-based entropic regularizer to favor smooth solutions over a graph induced by the data. The main contribution of this work is a computationally efficient, stochastic graph-regularization technique that u…

New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.

Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.

Study provides LDP for non self-similar stochastic volatility models.

This paper extends Heston model to fractional Brownian motion for option pricing.

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …

We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with trans…

We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described in [13] for the construction of mini-batches for stochastic gradient descent (SGD…

Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.

Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

Study examines surfaces with bounded fractional mean curvature, proving control over local parametrization.

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black-Scho…

The paper introduces a new stochastic volatility model with long-term memory and jumps.

Proposes a new metric for financial risk based on volatility's local deviations.

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

Model for valuing options on epidemic spread.

We develop a variational framework for SDEs driven by fractional noise.

Paper introduces a new method for risk-sensitive investment management using RL.

Formula for option pricing in a stochastic volatility model with jumps.

Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part, followed by a reasonable approximation we show that it is possible to cast the proble…

Defines a new process for financial modeling.

In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generaliz…

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…

In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift and fractional diffusion. Since the DO process is a semi-martingale,…

Study optimal partitions on spheres using fractional Q-curvature and variational methods.

Deep learning method improves myelin water fraction estimation.

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection phase is often ignored. In fact, in theoretical works most of the time assumptio…