arXiv research

This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are negligible in the short time limit.

Paper presents a unique method to recover signals from their bispectrum.

We derive the ODE of MAML and propose a new BI-MAML algorithm.

Paper solves Bayesian bandit problem with continuous-time limit and approximate policy.

Machine learning models are vulnerable to adversarial examples: small changes to images can cause computer vision models to make mistakes such as identifying a school bus as an ostrich. However, it is still an open question whether humans are prone to similar mistakes. Here, we address this question by leveraging recen…

Time-limited metaheuristics find near-optimal solutions for constrained portfolio optimisation.

We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options…

New RL algorithms adapt to time limits, improving task performance.

We obtain a lower bound for the diameter of a solution to the Ricci flow on a compact manifold with nonvanishing first real cohomology. A consequence of our result is an affirmative answer to Hamilton's conjecture that a product metric on $(S^{1}\times S^{n-1}$ cannot arise as a final time limit flow.

Diffusion means converge to extrinsic means for long times on spheres.

New MCMC method tackles label-switching problem for clustering.

In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on…

Study on Ricci flows of awesome homogeneous spaces, proving finite extinction time.

Method uses trinomial trees to price nontraditional options.

We apply the formalism of the continuous time random walk (CTRW) theory to financial tick data of the bond futures transacted in Korean Futures Exchange (KOFEX) market. For our case, the tick dynamical behaviors of the returns and volatility for bond futures are treated particularly at the long-time limit. The volatili…

We study the continuous time random walk theory from financial tick data of the yen-dollar exchange rate transacted at the Japanese financial market. The dynamical behavior of returns and volatilities in this case is particularly treated at the long-time limit. We find that the volatility for prices shows a power-law w…

We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled Kähler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson conjecture. We also obtain a necessary and sufficient condition for…

We show that three-dimensional homogeneous Ricci flow solutions that admit finite-volume quotients have long-time limits given by expanding solitons. We show that the same is true for a large class of four-dimensional homogeneous solutions. We give an extension of Hamilton's compactness theorem that does not assume a l…

We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the conver…

We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization. We prove that in the large particle limit the empirical measure of the particle s…

Semistatic trading strategies can be taken to limits in discrete time.

Improved prediction algorithm for 'easy' sequences with reduced regret.

We study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces $\mathbb{H}H^n$ and $\mathbb{H}P^n$. The characteristic functions of fixed-time marginals of these processes are computed and allows for the explicit description of their corresponding large-t…

A blockchain replaces central counterparties with time-consuming consensus protocols to record the transfer of ownership. This settlement latency slows cross-exchange trading, exposing arbitrageurs to price risk. Off-chain settlement, instead, exposes arbitrageurs to costly default risk. We show with Bitcoin network an…

We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the super-replication cost in these models are obtained and used to prove the limit the…

Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep learning settings admits a non-Gaussian, heavy-tailed behavior. This suggests tha…

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and Mézard have proposed an interesting model of economy [Bouchaud and Mézard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law …

We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain aroun…

We study the tick dynamical behavior of the bond futures in Korean Futures Exchange(KOFEX) market. Since the survival probability in the continuous-time random walk theory is applied to the bond futures transaction, the form of the decay function in our bond futures model is discussed from two kinds of Korean Treasury …

Study long-term asset liquidation behavior with external flows.

Develops a gradient flow for Muon optimizer, a method for optimization.

The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.

Constructs constant spacetime mean curvature surfaces for hyperboloidal initial data sets.

Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e. decision-makers are bounded in their rationality. Here we experimentally tested the predic…

We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via agents' excess demand functions, and the diffusion approximation approach is appl…

Study on how non-reversible diffusion processes affect homology on manifolds.

This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of …

We construct smooth solutions to Ricci flow starting from a class of singular metrics and give asymptotics for the forward evolution. The singular metrics heal with a set of points (of codimension at least three) coming out of the singular point. We conjecture that these metrics arise as final-time limits of Ricci flow…

The paper explores how score-driven models can approximate rough volatility.

In this study, we focus on the market clearing problem of Turkish day-ahead electricity market. We propose a mathematical model by extending the variety of bid types for different price regions. The commercial solvers may not find any feasible solution for the proposed problem in some instances within the given time li…

Study how untrained policies explore in RL environments.

The paper explores IL and LVR in AMMs, identifying three regimes and the effect of fees.

Optimizes data power control in cell-free networks for better spectral efficiency.

The paper examines how deep linear neural networks behave as they become infinitely wide.

Study optimizes portfolio liquidation strategies with complex market impacts.

This paper is the second part of a series of papers on noncommutative geometry and conformal geometry. In this paper, we compute explicitly the Connes-Chern character of an equivariant Dirac spectral triple. The formula that we obtain for which was used in the first paper of the series. The computation has two main ste…