Related papers: A C\`adl\`ag Rough Path Foundation for Robust Fina…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives.
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some…
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under…
The purpose of this note is to prove the It{\^o}-F\"ollmer formula for the c\`adl\`ag paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions. By this we mean, for example, that we do not…
We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…
Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we…
We present a non-probabilistic, path-by-path framework for studying path-dependent (i.e., where weight is a functional of time and historical time-series), long-only portfolio allocation in continuous-time based on [Chiu & Cont '23], where…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded…
A statistic based on increment ratios (IR) and related to zero crossings of increment sequence is defined and studied for measuring the roughness of random paths. The main advantages of this statistic are robustness to smooth additive and…
Backtests on historical data are the basis for practical evaluations of portfolio selection rules, but their reliability is often limited by reliance on a single sample path. This can lead to high estimation variance. Resampling techniques…
We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly,…
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly.…
This article provides a concise overview of some of the recent advances in the application of rough path theory to machine learning. Controlled differential equations (CDEs) are discussed as the key mathematical model to describe the…
In this paper, we study the robust optimal investment and risk control problem for an insurer who owns the insider information about the financial market and the insurance market under model uncertainty. Both financial risky asset process…
In this work, we generalise Gelfand-Yaglom-type methods in the vector case for the computation of Gaussian path integrals. The extension we propose allows to consider general second variation operators subject to different boundary…
Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.