Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
The paper develops methods to price derivatives in a time-varying, age-dependent market.
problem Pricing derivatives in a market with time-inhomogeneous volatility and age-dependent processes.
method Geometric Brownian motion model with time-varying volatility and age-dependent semi-Markov processes. Solves a non-local PDE and integral equation.
result Explicit expressions for derivative prices and hedging strategies are derived.
This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for time-inhomogeneous Markov processes. For stochastically continuous affine proce…
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
Efficient method for lookback option pricing under Markov models.
problem Pricing lookback options under Markov models.
method Model-free representations combined with numerical quadrature and Markov chain approximation.
result Efficient method applicable to various Markov models.
We propose two main applications of Gyöngy (1986)'s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based stochastic volatility mod…
A new ML algorithm solves complex economic control problems.
problem Solving high-dimensional, finite-horizon stochastic control problems in economics.
method Deep neural network representation of optimal policy functions with three key features.
result Efficiently solves various economic control problems including recursive utility and growth models.
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the use of the numerical scheme for Heston or SABR type stochastic volatility model…
This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigro…
Develops time-inhomogeneous polynomial processes for better model calibration and seasonality capture.
problem Calibration to market prices and seasonality in term-structure models.
method Introduces time-inhomogeneous polynomial processes with time-dependent coefficients and characterizes them using semimartingale characteristics. Alternative numerical approximations using Magnus series are explored.
result Matrix exponentials are not sufficient for computing moments in time-inhomogeneous polynomial processes, necessitating alternative numerical methods.
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
problem Floating exercise boundaries in time-inhomogeneous models with negative interest rates or yields.
method Semi-analytical approach for pricing American options.
result Specialized pricing methodologies are required for models with floating exercise boundaries.
This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to the approach by Carmona and Nadtochiy (2009) and related to the recent contribution Carmona and Nadtochiy (2012) by the same authors, the key parametrisation of our app…
New method for pricing European options in rough LSV models.
problem Pricing European options in non-Markovian local stochastic volatility models.
method Conditional LSV dynamics, rough path theory, rough partial differential equations (RPDEs).
result Established a PDE pricing method for non-Markovian models.
Neural Markov models improve time series analysis by balancing deep learning and classical models.
problem Modeling non-stationary time series with high data sparsity.
method Hybrid approach using neural networks to parameterize stochastic matrices, estimating time-inhomogeneous Markov chains.
result Reduction of Chapman-Kolmogorov discrepancy and superior likelihood in financial markets.
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over…
Study magnetic field evolution in inhomogeneous axion stars.
problem Magnetic field evolution in axion stars with spatial inhomogeneity.
method Derived new induction equation for magnetic field, analyzed CS waves interactions, and considered compact domain effects.
result Spatial inhomogeneity of pseudoscalar field significantly affects magnetic field evolution.
In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficienc…
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio α=p/N of the number p o…
Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distribu…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are switching. We argue that such a model captures well the stock price dynamics under per…
The paper analyzes convergence of Langevin dynamics with time-dependent metrics.
problem Analyzing convergence of Langevin dynamics with time-dependent metrics.
method Formulated a modified gradient flow of the Kullback-Leibler divergence, selected a time-dependent relative Fisher information functional, and developed a time-dependent Hessian matrix condition.
result Proved convergence conditions for various Langevin dynamics.
We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S^m with S^2 bundles over K_{2n}, for m>1. Additionally,…
Develops a new method for pricing barrier options in time-dependent Heston model.
problem Pricing barrier options in a time-dependent Heston model with stochastic volatility.
method General Integral Transforms (GIT) method for a two-dimensional integral representation.
result Shows that the GIT method can be extended to two drivers with inhomogeneous correlation.
Probabilistic proof of smooth boundaries in optimal stopping problems.
problem Continuous differentiability of time-dependent optimal boundaries in optimal stopping problems.
method Local probabilistic arguments for a wider range of conditions.
result First probabilistic proof of continuous differentiability under general conditions.
This paper develops methods for pricing American Parisian options under general Markov models.
problem Pricing American Parisian options with various types and payoff functions.
method General approaches using CTMC approximation for time-inhomogeneous Markov models, including state augmentation and variational inequalities.
result Efficient algorithms for pricing American Parisian options confirmed with numerical experiments.
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
New risk metric for RL in finance considers time splits of returns.
problem Optimizing financial decisions with a balance between return and risk.
method Developed a new risk metric for reinforcement learning that allows for flexible target levels of rewards over time.
result Proposed risk metric optimizes for arbitrary time splits of returns, improving upon classical risk measures.
Unified method detects and localizes anomalous cliques in inhomogeneous networks.
problem Detect and localize anomalous cliques in inhomogeneous networks.
method Unified method based on egonets for detection and localization.
result Unified method can detect and localize anomalous cliques in inhomogeneous networks.
The goal of this paper is to specify dynamic term structure models with discrete tenor structure for credit portfolios in a top-down setting driven by time-inhomogeneous Lévy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion and prici…
Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.
problem Understanding deformations of quaternionic Kähler manifolds.
method Proved one-loop deformation of quaternionic Kähler manifolds are locally inhomogeneous.
result Full isometry group of one-loop deformations has cohomogeneity one.
We introduce a new parameter to measure the inhomogeneity of training datasets.
problem The need for non-stationary models in supervised learning.
method We introduce a new parameter, the inhomogeneity parameter, to measure the inhomogeneity of training datasets.
result A training set with a non-zero inhomogeneity parameter requires a non-stationary model for accurate predictions.
Researchers describe a specific type of submanifolds in Euclidean space.
problem Understanding inhomogeneous almost symmetric submanifolds.
method Completely describing submanifolds as unions of parallel symmetric submanifolds.
result Described inhomogeneous properly embedded almost symmetric submanifolds as unions of symmetric submanifolds.
New financial models use tempered stable subordination for better correlation dynamics.
problem Building financial models with better correlation dynamics.
method Introducing tempered stable Sato subordinators and additive inhomogeneous processes.
result The new process has time-dependent correlation, improving fit for financial data.
Sharp threshold found for Frechet mean of inhomogeneous graphs.
problem Finding the Frechet mean of inhomogeneous Erdos-Renyi random graphs.
method Thresholding the expected adjacency matrix of the ensemble.
result The Frechet mean graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold.
The new framework for finance is proposed. This framework based on three known approaches in econophysics. Assumptions of the framework are the following: 1. For the majority of situations market follows non-arbitrage condition. 2. For the small number of situations market influenced by the actions of big firms. 3. If …
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
The paper studies inhomogeneous isoparametric hypersurfaces in pseudo-spheres.
problem Investigating inhomogeneous isoparametric hypersurfaces in pseudo-sphere.
method Construction of Clifford systems and analysis of isoparametric hypersurfaces.
result Connected isoparametric hypersurfaces of OT-FKM-type in pseudo-spheres are inhomogeneous under specific conditions.
Efficiently matches random graphs with inhomogeneous edge probabilities.
problem Matching latent vertex correspondence between two correlated random graphs with inhomogeneous edge probabilities.
method Inspired by Ding et al. (2021), an efficient matching algorithm is developed with conditions on minimal average degree and minimal correlation.
result An efficient matching algorithm is obtained as long as the minimal average degree is at least Ω(log2n) and the minimal correlation is at least 1−O(log−2n). Two families of curvature inhomogeneous manifolds with constant Ricci eigenvalues are constructed.
problem Constructing curvature inhomogeneous Riemannian manifolds with constant Ricci eigenvalues.
method Derived from Einstein warped products and Riemannian Schwarzschild--Tangherlini manifold.
result Admits local isometric immersions and isometric embeddings of minimum codimension.
Unique inhomogeneous ruled hypersurface found in complex hyperbolic space.
problem Classifying ruled real hypersurfaces with constant norm.
method Analyzing nonflat complex space forms, proving existence and uniqueness.
result Existence of a unique inhomogeneous example in complex hyperbolic space.
We construct explicit global symplectic coordinates for the Calabi's inhomogeneous Kaehler-Einstein metric on tubular domains.
Study on solutions of degenerate equations on manifolds, linking behavior to geometry and decay rates.
problem Behavior of solutions to degenerate parabolic equations on manifolds with inhomogeneous density.
method Analysis of Cauchy problem on Riemannian manifolds, considering weight function as capacitary coefficient.
result Estimates of vanishing rate and finite speed of propagation in subcritical ranges, universal bounds and blow-up in supercritical ranges.
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. By means of the limiting absorption principle, a Fredholm alterna…
New hypergraph clustering method assigns different costs to hyperedge cuts.
problem Hypergraph partitioning assumes uniform costs for different hyperedge cuts.
method Inhomogeneous hypergraph partitioning assigns different costs to different hyperedge cuts.
result Inhomogeneous partitioning offers significant performance improvements in various applications.
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our re…
Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.
problem Recovering signals through an inhomogeneous low-rank matrix channel.
method Derive and analyze an approximate message-passing algorithm (AMP) and a spectral method.
result The AMP iteration matches the conjectured optimal computational phase transition.
The study finds that asset correlations underestimated when exposure pools are not homogeneous.
problem Systematic error in estimating asset correlations from default data due to exposure pool inhomogeneity.
method Investigates the effect of exposure pool homogeneity on asset correlation estimation from default time series.
result Asset correlation is systematically underestimated when exposure pools are inhomogeneous, especially if PD is spread out.