Related papers: Roughness Signature Functions
The signature of a path is a sequence, whose $n$-th term contains $n$-th order iterated integrals of the path. These iterated integrals of sample paths of stochastic processes arise naturally when studying solutions of differential equation…
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…
In this chapter we first briefly review the existing approaches to hedging in rough volatility models. Next, we present a simple but general result which shows that in a one-factor rough stochastic volatility model, any option may be…
We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a…
In this paper, a novel signature of human action recognition, namely the curvature of a video sequence, is introduced. In this way, the distribution of sequential data is modeled, which enables few-shot learning. Instead of depending on…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and…
Volatility prediction in the financial market helps to understand the profit and involved risks in investment. However, due to irregularities, high fluctuations, and noise in the time series, predicting volatility poses a challenging task.…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
The perception and recognition of the surroundings is one of the essential tasks for a robot. With preliminary knowledge about a target object, it can perform various manipulation tasks such as rolling motion, palpation, and force control.…
This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump-diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in…
Speeded Up Robust Features (SURF) has emerged as one of the more popular feature descriptors and detectors in recent years. Performance and algorithmic details vary widely between implementations due to SURF's complexity and ambiguities…
Measuring systemic risk or fragility of financial systems is a ubiquitous task of fundamental importance in analyzing market efficiency, portfolio allocation, and containment of financial contagions. Recent attempts have shown that…
Runtime Verification is a lightweight formal verification technique. It is used to verify at runtime whether the system under analysis behaves as expected. The expected behaviour is usually formally specified by means of properties, which…
We extend the signature-based primal and dual solutions to the optimal stopping problem recently introduced in [Bayer et al.: Primal and dual optimal stopping with signatures, to appear in Finance & Stochastics 2025], by integrating…
Stability guarantees have emerged as a principled way to evaluate feature attributions, but existing certification methods rely on heavily smoothed classifiers and often produce conservative guarantees. To address these limitations, we…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
We describe a Matlab routine that allows us to estimate the jumps in financial asset prices using the Threshold (or Truncation) method of Mancini (2009). The routine is designed for application to five-minute log-returns. The underlying…