arXiv research

Study on Yamabe flow on manifolds with singularities, proving removability.

The Ricci flow preserves product structures with instantaneous curvature bounds.

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [23, 11], this completes the well…

We use a first-order energy quantity to prove a strengthened statement of uniqueness for the Ricci flow. One consequence of this statement is that if a complete solution on a noncompact manifold has uniformly bounded Ricci curvature, then its sectional curvature will remain bounded for a short time if it is bounded ini…

In this work, we obtain some existence results of Chern-Ricci Flows and the corresponding Potential Flows on complex manifolds with possibly incomplete initial data. We discuss the behaviour of the solution as $t\rightarrow 0$. These results can be viewed as generalization of an existence result by Giesen and Topping f…

A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.

Study gap phenomenon in flat manifolds with Ricci curvature.

We prove global existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension $m\geq3$ starting from any smooth, conformally hyperbolic initial metric. We do not require initial completeness or curvature bounds. With the same methods, we show rigidity of hyperbolic space under the Yamabe…

A new model prices assets considering market microstructure effects.

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.

We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can be described by a three-dimensional system of backward stochastic differential eq…

Unified framework for optimal liquidation with small market impact and semimartingale strategies.

The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.

The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged inst…

New framework IDOL identifies latent causal processes with instantaneous relations from time series data.

Let $\overline{M}$ be a compact complex manifold with smooth Kähler metric $η$, and let $D$ be a smooth divisor on $\overline{M}$. Let $M=\overline{M}\setminus D$ and let $\hatω$ be a Carlson-Griffiths type metric on $M$. We study complete solutions to Kähler-Ricci flow on $M$ which are comparable to $\hatω$, starting …

This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrag…

New formula for instantaneous frequency in unbalanced systems.

New formulation tackles arbitrage in volatile markets using eigenvalue bounds.

An arbitrage strategy allows a financial agent to make certain profit out of nothing, i.e., out of zero initial investment. This has to be disallowed on economic basis if the market is in equilibrium state, as opportunities for riskless profit would result in an instantaneous movement of prices of certain financial ins…

iCITRIS learns causal variables from interactive systems with instantaneous effects.

Aggregation distorts causal discovery results but recovery is possible with partial linearity or prior.

Study compares Fourier estimators to mitigate asynchrony effects in finance.

We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by i…

This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed process can match exactly the risk-neutral distributions implied by both spot va…

Paper revises power theory using classical mechanics concepts.

Instantaneous volatility estimated from traded volume and spread.

Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.

Modeling continuous movement of entities in latent space for interaction timing.

We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a multivariate counting process with stochastic intensities. The interest rate, drift, …

Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current …

Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic vol…

A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.

The paper develops an expansion for optimizing portfolios with small quadratic transaction costs.

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model behavior: the volatility pr…

Rhino learns causal relationships from time series data with history-dependent noise.

Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during tre…

Extends option pricing model to incorporate market factor dynamics.

Study optimal execution in a transient price impact model with multiple traders.

Estimates chirp signal frequencies using probabilistic models.

In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations wi…

New model identifies regimes in non-stationary data.

A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of ne…

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…

We compare optimal static and dynamic solutions in trade execution. An optimal trade execution problem is considered where a trader is looking at a short-term price predictive signal while trading. When the trader creates an instantaneous market impact, it is shown that transaction costs of optimal adaptive strategies …

To convert standard Brownian motion $Z$ into a positive process, Geometric Brownian motion (GBM) $e^{βZ_t}, β>0$ is widely used. We generalize this positive process by introducing an asymmetry parameter $α\geq 0$ which describes the instantaneous volatility whenever the process reaches a new low. For our new process, …

An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time inte…