arXiv research

New method reduces errors in pricing and sensitivities for discontinuous payoffs.

Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.

This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.

The Monte Carlo pathwise sensitivities approach is well established for smooth payoff functions. In this work, we present a new Monte Carlo algorithm that is able to calculate the pathwise sensitivities for discontinuous payoff functions. Our main tool is to combine the one-step survival idea of Glasserman and Staum wi…

We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …

A new method in finance without probabilities or integrals.

The paper discovers the family of identically-derived Euclidean one-parameter even-dimensional differential linear operators with unique eigenproperties, which prove to be inherently related to the emergent characterizations of fundamental building blocks of embedded minimal surfaces and the Nitsche conjecture proof.

Quantum machine learning solves high-dimensional PDEs with lower variance and improved accuracy.

Proposes a new method for estimating non-pathwise differentiable functional parameters.

We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itō calculus. Price trajectories are $d$-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategie…

This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.

Efficient inference for adaptive data with directional stability condition.

Pathwise uniqueness shown for specific stochastic equations.

Develops pathwise analysis for log-optimal portfolios using rough paths theory.

Develops portfolio theory without probabilistic analysis, focusing on pathwise decomposition.

Second-order optimization speeds up deep hedging for complex options.

New measure captures differences across entire distributions of counterfactual outcomes.

A new approach to continuous-time universal portfolios using pathwise Itô calculus.

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; …

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…

ULFS-KDPE estimates parameters efficiently without influence functions.

The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: {\it warm start initialization}, {\it active set updating}, and {\it …

New machine learning methods solve complex PDEs with improved accuracy.

We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of Föllmer's pathwise Itô calculus and works for portfolios generated from functions that may depend on the current states of the market port…

This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…

We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the inequalities to derive …

This paper gives several simple constructions of the pathwise Ito integral $\int_0^tφdω$ for an integrand $φ$ and a price path $ω$ as integrator, with $φ$ and $ω$ satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither $φ$ nor $ω$ are assumed to be paths of stochast…

Study shows rate of convergence for particle approximation of PDEs in Wasserstein space.

This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.

This work introduces efficient sampling methods for Gaussian processes by focusing on pathwise conditioning.

MuRiT efficiently computes multi-parameter persistence barcodes.

We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the transport equation to construct adaptive control variates that can be used to construct…

A new reinforcement learning method uses model derivatives to improve policy optimization.

We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterizati…

We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical analysis, and an implied volatility consistent with options priced with the model. The…

This paper deals with the computation of second or higher order greeks of financial securities. It combines two methods, Vibrato and automatic differentiation and compares with other methods. We show that this combined technique is faster than standard finite difference, more stable than automatic differentiation of se…

The paper optimizes bridge-type estimators for sparse models using pathwise methods.

We consider a class $\mathscr{X}$ of continuous functions on $[0,1]$ that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in $\mathscr{X}$ admits a linear pathwise quadratic variatio…

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 squared volatility, or `cumulative variance'. In the new framework, corresponding p…

Study shows how market firm capitalization models converge to stochastic PDE solutions.

Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is $α$-Hölder …

Exact simulation method for market impact estimation under various execution strategies.

NM-PPG optimizes adaptive feature acquisition in POMDPs for better predictions.

Develops a method for solving optimal stopping problems with multiple exercise rights.

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised vari…

Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

Differential ML combines AAD with ML for fast, accurate financial derivatives pricing and risk management.