Study forward investment performance in semimartingale markets with stochastic factors.
problem Investigate forward investment performance in incomplete semimartingale markets with power risk preferences and stochastic integrated factors.
method Develop necessary and sufficient conditions for FIPP existence, use integral representations, and solve ill-posed HJB equations.
result Explicit constructions for time-monotone FIPPs in semimartingale models, generalizing from Brownian to semimartingale markets.
We study the forward price dynamics in commodity markets realized as a process with values in a Hilbert space of absolutely continuous functions defined by Filipović. The forward dynamics are defined as the mild solution of a certain stochastic partial differential equation driven by an infinite dimensional Lévy proces…
Study shows Skorokhod insider outperforms forward insider in logarithmic utility maximization.
problem Maximizing logarithmic utility for an insider with different anticipating techniques.
method Comparison of Russo-Vallois forward and Skorokhod integrals.
result Skorokhod insider outperforms forward insider in logarithmic utility maximization.
China uses two Renminbi markets to hedge cross-border risks, leading to a price discrepancy.
problem China's two Renminbi markets (onshore and offshore) create a price discrepancy for currency forwards.
method Joint equilibrium model for spot and forward trading with transaction costs and segmented supply.
result The model explains the observed forward price discrepancy in terms of offshore liquidity stress.
Study compares different integrals for optimal portfolio optimization with insider information.
problem Optimizing portfolios in a financial market with insider information.
method Anticipating stochastic calculus and various integrals (Russo-Vallois forward, Ayed-Kuo, Hitsuda-Skorokhod).
result The Hitsuda-Skorokhod and Ayed-Kuo integrals do not provide a financially meaningful investment strategy.
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM-model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theo…
For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability.
This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present …
Established PFPPs in complete markets, solving integral equations.
problem Existence of Predictable Forward Performance Processes in complete markets.
method Solving a one-period integral equation using Fourier transform for tempered distributions.
result Closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic.
Efficiently simulates SABR model with novel sampling methods.
problem Sampling integrated variance and terminal forward price in SABR model.
method Moment-matched shifted lognormal approximation for integrated variance, CEV approximation for terminal forward price.
result Enhanced simulation scheme is highly efficient, accurate, and reliable.
Two geometric tests for forward-flatness are shown to be dual.
problem Checking forward-flatness in discrete-time systems.
method Two geometric tests based on involutive distributions and integrable codistributions.
result The two tests are dual to each other.
New PFPPs based on rank-dependent utility for better performance control.
problem Improving performance prediction in systems with short-term control.
method Introduces rank-dependent PFPPs, solves integral equations via Volterra theory.
result Existence of rank-dependent PFPPs under specific market conditions.
FORK improves model-free reinforcement learning performance.
problem Improving model-free reinforcement learning performance.
method Introducing a new forward-looking Actor (FORK) for Actor-Critic algorithms.
result FORK significantly improves performance in various environments.
A new dual test for forward-flatness simplifies computations.
problem Checking forward-flatness in discrete-time systems.
method A unique sequence of integrable codistributions.
result Computational efficiency and comparison with dynamic feedback linearization.
Pricing Bermudan swaptions with few exercise dates using analytic methods.
problem Pricing Bermudan swaptions with few exercise dates
method Analytic decomposition and backward induction under rolling forward measures
result Pricing formulas with decomposition and boundary linearity
New algorithm optimizes nonlinear SDEs online with convergence guarantees.
problem Optimizing nonlinear stochastic differential equations (SDEs) is computationally challenging.
method Forward propagation algorithm that solves an SDE derived using forward differentiation.
result Convergence theorem for nonlinear dissipative SDEs with bounds on stochastic fluctuations.
We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.
Forward hedging reshapes incentive provision in firms.
problem How does forward hedging affect incentive provision in firms?
method We consider a CARA framework to jointly characterize optimal production, compensation, and static hedging in equilibrium.
result Delegation and external hedging are partial substitutes, and delegation can increase firm value even when the agent is more risk averse.
Deep-learning method solves BSVIEs and coupled systems.
problem High-dimensional, time-inconsistent stochastic control problems.
method Trains a neural network to approximate solution fields directly.
result Non-asymptotic error bound and scalable performance.
Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions…
Deep learning calibrates HJM forward curves for commodity options pricing.
problem Calibrating HJM forward curves for accurate option pricing in commodity markets.
method Introduced a neural network to approximate true option prices from model parameters, calibrated using observed option prices.
result Neural network calibration yields high accuracy in recovering option prices, even with model parameter approximation loss.
The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump…
Forward construction of vacuum initial data with limited decay
problem Constructing solutions of the Einstein vacuum constraint equations with limited decay
method Free data formalism and new gauge condition
result Constructing general solutions with minimal and even borderline decay
Honest traders can outperform insiders in a Black-Scholes market with positive probability.
problem Comparing the performance of honest and insider traders in a financial market.
method Using anticipating stochastic calculus and forward integral analysis of the Doléans-Dade exponential process.
result The honest trader can achieve higher logarithmic utility and wealth than the insider with positive probability.
We propose here a new discretization method for a class continuum gauge theories which action functionnals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for…
A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. …
We provide approximations for VIX futures and options in forward variance models.
problem Modeling VIX futures and options in forward variance models.
method Weak approximations and explicit formula derivation for VIX futures and options.
result Explicit combinations of Black-Scholes prices and greeks for option price approximations.
New approach avoids restrictive assumptions for optimal portfolio in default risk scenarios.
problem Optimal portfolio optimization under default risk when traditional techniques are not applicable.
method Alternative approach using forward integration to avoid Jacod density hypothesis.
result Weaker intensity hypothesis is the appropriate condition for optimality in logarithmic utility.
Bayesian units improve speech recognition with minimal parameters.
problem Improving speech recognition models with fewer parameters.
method Derived Bayesian recurrent units integrated into deep learning frameworks.
result Adding Bayesian units improves speech recognition performance.
The paper shows how Sobolev maps affect currents in metric spaces.
problem Understanding how Sobolev maps affect currents in metric spaces.
method Proving that a Sobolev map pushes almost every compactly supported integral current to an Ambrosio-Kirchheim integral current.
result The paper proves an isoperimetric inequality for Sobolev mappings relative to bounded, closed, and additive cochains.
Combines historical and market data for better portfolio selection.
problem Improving portfolio selection through diverse information integration.
method Bayesian learning via Gaussian mixture model to harmonize historical and market data.
result The method enhances forecasting accuracy and robustness across various capital markets.
New IBP formulae for rough stochastic Volterra processes.
problem Deriving IBP formulae for path-dependent stochastic Volterra processes.
method Developed a new fractional IBP formula that interpolates between standard and Bismut-Elworthy-Li formulae.
result For rough noise, the expectation is differentiable along constant directions under certain Hölder continuity conditions.
Physics-informed deep learning for PDEs solves forward and inverse problems efficiently.
problem Solving forward and inverse problems in parametric PDEs efficiently and accurately.
method Physics-informed deep latent variable model (PDDLVM) combining deep neural networks, probabilistic modelling, and variational inference.
result Achieves up to three orders of magnitude speed-up compared to traditional FEM while providing coherent uncertainty estimates.
Improves predictions by integrating forward-looking views into dynamic factor models.
problem Poor forecasts from historical data when dynamics change.
method Combines historical data with forward-looking views using a dynamic factor model.
result Derives optimal portfolio strategies influenced by both myopic and intertemporal factors.
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon b…
New HMC method handles features in POS tagging, outperforming MEMM.
problem HMC struggles with arbitrary features in POS tagging.
method Introduced Entropic Forward-Backward (EFB) probabilities to compute HMC restorations.
result EFB-based HMC outperforms MEMM in POS tagging.
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In…
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to O(ε−2log2(ε)) and asymptotically optimal O(ε−2). FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
problem Solving Partial Integro-Differential Equations and Forward-Backward Stochastic Differential Equations with Jumps.
method FBSJNN framework using a single neural network for both solution approximation and non-local integral.
result FBSJNN achieves numerical solutions with a relative error of 10−3, demonstrating efficiency. Bayesian inference for inverse problems using mean-shift interacting particles
problem Bayesian inference for inverse problems
method Amortized mean-shift interacting particles
result Improves accuracy of Bayesian inference by reducing the number of samples needed
Enhances uncertainty modeling in random PDEs using PINNs and generative models.
problem Uncertainty in complex systems modeled by random PDEs.
method Combines Physics-Informed Neural Networks (PINNs) with generative modeling techniques.
result Systematic control of uncertainty with maintained predictive accuracy.
ACI identifies cause-effect relationships and causal influence ranges in dynamical systems.
problem Detecting and quantifying causal influence ranges in complex systems.
method Bayesian data assimilation and assimilative causal inference (ACI) to trace causes back from observed effects.
result Mathematically rigorous formulations of forward and backward causal influence ranges (CIRs) for nonlinear dynamical systems.
We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an efficient and stable treatment of constraints. The key observation is that the stabili…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid G may be described in terms of Lagrangian implicit difference equations …
Language grounded image understanding tasks have often been proposed as a method for evaluating progress in artificial intelligence. Ideally, these tasks should test a plethora of capabilities that integrate computer vision, reasoning, and natural language understanding. However, rather than behaving as visual Turing t…
We use path integrals to calculate hedge parameters and efficacy of hedging in a quantum field theory generalization of the Heath, Jarrow and Morton (HJM) term structure model which parsimoniously describes the evolution of imperfectly correlated forward rates. We also calculate, within the model specification, the eff…
Breiman's two cultures reconciled through blending statistical thinking.
problem Tension between parametric statistical and machine learning approaches.
method Establishing a link between parametric statistical and machine learning frameworks.
result Integrated statistical thinking can bridge the gap between two cultures.
A new algorithm solves high-dimensional nonlinear BSDEs efficiently.
problem Solving high-dimensional nonlinear backward stochastic differential equations (BSDEs).
method Transformed BSDE into a differential deep learning problem using Malliavin calculus. Discretized integrals using Euler-Maruyama method. Approximated solution with three deep neural networks. Optimized parameters using a differential learning loss function.
result Our algorithm is more accurate and faster than other methods.