arXiv research

This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.

The paper improves evolutionary computation by optimizing selection rates.

Study evaluates how changes in mobility affect COVID-19 case rates.

Researchers solve a market model with stochastic interest rate using worst case approach.

In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend also on other stochastic factors. Ou…

The paper tackles robust control for insurance contracts under uncertain transition rates.

In this work, I generalize Merton's approach of pricing risky debt to the case where the interest rate risk is modeled by the CIR term structure. Closed form result for pricing the debt is given for the case where the firm value has non-zero correlation with the interest rate. This extends previous closed form pricing …

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Sle…

In [6], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture is always true for the case of ideal Coxeter polyhedra in $\mathbb{H}^3$. We also find out the ideal Coxeter polyhedron in $\mathbb{H}^3…

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, firstly when volatility is taken to be a function of the forward rates…

Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.

New formula classifies product reviews into higher and lower ratings based on sentiment analysis.

This paper investigates the relevance of the No-Ponzi game condition for public debt (i.e. the public debt growth rate has to be lower than the real interest rate, a necessary assumption for Ricardian equivalence) and of the transversality condition for the GDP growth rate (i.e. the GDP growth rate has to be lower than…

We extend Dupire's formula for stochastic interest rates and local volatility.

Optimal rates for vector-valued regression on various norms.

Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes. In contrast, SGD's final iterate behavior has received much less attention desp…

Paper analyzes faster convergence rates for reinforcement learning from offline data.

Study examines how COVID-19 affected India's exchange rates and stock market.

Flexible model captures commodity skews with maturity effects.

A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives \emph{a priori} as a Gauss--Markov process $\boldsymbol{X}$, which is…

Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.

Proves lower discount rates are needed for future losses.

We provide analytical pricing formula of corporate defaultable bond with both expected and unexpected default in the case with stochastic default intensity. In the case with constant short rate and exogenous default recovery using PDE method, we gave some pricing formula of the defaultable bond under the conditions tha…

Semi-supervised EM improves convergence rate with labeled samples.

New theorem for generalized group sparsity improves consistency and convergence rates.

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather use historical stock prices and an a priory given distribution of the appreciati…

New proof shows not all Salem numbers are growth rates of Coxeter groups.

We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…

New neural network rates for unbounded domains with weighted Sobolev spaces.

The paper analyzes kNN density estimation's convergence rates under different conditions.

The dynamical behavior of the currency exchange rate after its large-scale catastrophe is discussed through a case study of the rate of Russian rubles to US dollars after its crash in 2014. It is shown that, similarly to the case of the stock market crash, the relaxation is characterized by a power law, which is in ana…

We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…

The article calculates the $\mathbb{F}$-convergence rate for Ricci flows with closed and smooth tangent flows.

This article considers the problem of multi-group classification in the setting where the number of variables $p$ is larger than the number of observations $n$. Several methods have been proposed in the literature that address this problem, however their variable selection performance is either unknown or suboptimal to…

Improved learning rates with new smoothness measure.

Study on convergence rate of $Q$-curvature flow in 6 dimensions.

We prove new fast learning rates for the one-vs-all multiclass plug-in classifiers trained either from exponentially strongly mixing data or from data generated by a converging drifting distribution. These are two typical scenarios where training data are not iid. The learning rates are obtained under a multiclass vers…

We consider an individual or household endowed with an initial capital and an income, modeled as a deterministic process with a continuous drift rate. At first, we model the discounting rate as the price of a zero-coupon bond at zero under the assumption of a short rate evolving as an Ornstein-Uhlenbeck process. Then, …

New methods boost first-order optimization with faster rates.

This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the continuous diffusion process associated with the algorithm converges exponentially fa…

Study compares ZBDT model to BDT for financial derivatives valuation.

Optimal learning rate schedules derived for various tasks.

Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone loss functions, optimized on linearly separable data. Previous works assumed eit…

Unified algorithm solves convex optimization problems with optimal rates.

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of function values are available, algorithms for $d$-dimensional optimization that use …

This paper studies universal rates of ERM for binary classification under agnostic learning.

Paper analyzes convergence rates of compressed LSR algorithms in federated learning.