A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order for the theory to be self-consistent. The replicating methods in existing finance …
A stochastic model helps maintain insufficiently funded pension funds.
Quantum computing techniques applied to Monte Carlo simulations in finance.
The objective of the note is to remind readers on how self-financing works in Quantitative Finance. The authors have observed continuing uncertainty on this issue which may be because it lies exactly at the intersection of stochastic calculus and finance. The concept of a self-financing trading strategy was originally,…
Alternative finance models from physics for non-equilibrium systems.
Gauge symmetries explain the emergence of Merton-Garman equation from Black-Scholes in finance.
FinFlowRL learns from experts to optimize financial control in changing markets.
Unified approach to stochastic Volterra systems' deviations.
FinFlowRL combines imitation and reinforcement learning for better financial control.
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
Clarifies when solutions to stochastic PDEs stay near given subsets.
Quantum algorithms speed up financial model calculations.
Model shows how discount rates affect intergenerational equity in climate mitigation.
In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in part…
Quantum computing promises to revolutionize finance, especially in optimization and modeling.
Develops a new solver for optimizing with stochastic dominance constraints.
New optimal investment strategies for finance and insurance using Hawkes-based models.
Neural SDEs reduce variance in stochastic simulations.
We present examples of agent-based and stochastic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in behavior. Microscopic and macroscopic versions of herding model proposed by Kirm…
New algorithm tackles optimization problems with discontinuous gradients in finance and insurance.
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and Rásonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to the usual investment in financial assets, we assume that the agents can invest part …
We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the causality in the evolution of dependent stochastic variables. We demonstrate this pr…
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
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 al.) considers fluctuations around this equilibrium state by introducing a relaxati…
New method samples from time-integrated stochastic bridges using neural networks.
New methods solve complex PDEs with mixed boundary conditions.
These are course notes on the application of SDEs to options pricing. The author was partially supported by NSF grant DMS-0739195.
This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatil…
Paper presents a new computational technique for finance using ERM and neural networks.
This overview article concerns the notion of fractional smoothness of random variables of the form , where is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance main…
NeuralChaos efficiently approximates complex stochastic processes.
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset …
In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic differential equations (FBSDE) final-value or control problems, how these final val…
The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.
Survey revisits Bachelier and Dupire, highlighting optimal transport's role.
Simplified calculus for stochastic processes simplifies complex financial calculations.
Two deep learning algorithms solve utility maximisation problems in finance.
Study provides LDP for non self-similar stochastic volatility models.
We consider the structure functions S^(q)(T), i.e. the moments of order q of the increments X(t+T)-X(t) of the Foreign Exchange rate X(t) which give clear evidence of scaling (S^(q)(T)~T^z(q)). We demonstrate that the nonlinearity of the observed scaling exponent z(q) is incompatible with monofractal additive stochasti…
Investigates financial and economic systems using statistical mechanics and information theory.
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous structure as the Black-Scholes model, the widely popular option pricing model in stochas…
Extends insurance-finance arbitrage concept to include model uncertainty.
The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a general tool for forecasts and simulations without the need to identify/assume a speci…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically eval…
Survey of RL in finance, tackling complex decision-making.
Enhances financial optimization under model uncertainty using subsampling.