Proves global well-posedness for superquadratic BSDEs without Markovian assumption.
problem Global well-posedness of multidimensional superquadratic BSDEs without Markovian assumption.
method Interplay between local well-posedness of FBSDEs and backward iterations of superquadratic BSDEs.
result Global well-posedness of superquadratic BSDEs proved.
Deep signature algorithm for pricing path-dependent options.
problem Pricing path-dependent options with complex payoff functions.
method Extended backward scheme for state-dependent FBSDEs with reflections, incorporating signature layer for path-dependent FBSDEs.
result Convergence analysis of the algorithm with explicit dependence on truncation order and neural network approximation errors.
Unified framework for inference in complex nonlinear processes.
problem Challenges in inferring nonlinear continuous stochastic processes with sparse observations and complex topologies.
method Neural Backward Filtering Forward Guiding (NBFFG) framework that constructs a variational posterior using a proxy linear-Gaussian process.
result Empirical results show NBFFG outperforms baselines on synthetic benchmarks and high-dimensional phylogenetic analysis tasks.
We show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most 2. From this it follows that the Hausdorff distance between any two surgery paths with the same initial sphere system and same target sphere system is at most 4. Our proof relies on understanding how su…
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -- …
Recurrent neural networks like long short-term memory (LSTM) are important architectures for sequential prediction tasks. LSTMs (and RNNs in general) model sequences along the forward time direction. Bidirectional LSTMs (Bi-LSTMs) on the other hand model sequences along both forward and backward directions and are gene…
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
Transformers learn multi-step reasoning through gradient descent.
problem Understanding how transformers solve symbolic multi-step reasoning tasks.
method Theoretical analysis of gradient descent dynamics and multi-phase training.
result Trained one-layer transformers can solve both backward and forward reasoning tasks with generalization guarantees.
The paper tackles robust control for insurance contracts under uncertain transition rates.
problem Maximizing utility in insurance contracts with uncertain transition rates.
method Novel robust utility maximization problem under bounded cumulative transition rate uncertainty, using worst-case scenario analysis.
result Existence and uniqueness of worst-case and best-case reserves for insurance contracts.
Generative Flow Networks solve shortest path problems in graphs.
problem Finding shortest paths in graphs.
method Generative Flow Networks with flow regularization.
result Training a GFlowNet can solve pathfinding problems in arbitrary graphs.
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This val…
In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple (Y,Z,ψ) where Y is a semimartingale, and (Z,ψ) are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of …
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
problem Solving FBSDEs with state and path dependent features.
method Incorporates deep signature/log-signature transformation into RNN model.
result Improves accuracy and training time compared to existing methods.
Deep learning solves high-dimensional quadratic hedging problems.
problem High-dimensional incomplete markets with mean-variance and local risk minimization.
method Deep learning-based BSDE solver for optimal hedging strategies.
result High-dimensional quadratic hedging is efficiently computed with deep learning.
Neural networks can approximate gradient of smooth functions, but with limitations.
problem Approximating gradient of smooth functions using neural networks.
method Proving limitations of neural networks with more than one hidden layer and introducing implicit parametrization.
result Neural networks with more than one hidden layer can only represent one feature in their first hidden layer.
New method for hedging path-dependent options with price impact using probabilistic arguments.
problem Hedging of path-dependent options with price impact.
method Dual formulation using probabilistic arguments, proving existence of perfect hedging portfolios.
result Existence of a perfect hedging portfolio for path-dependent options with price impact.
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets…
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over the graph. When applying the proximal gradient algorithm to solve this problem, t…
This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i…
URGE improves diffusion model quality without gradients or Hessian.
problem Improving sample quality in diffusion models without gradient evaluations.
method Path-wise importance reweighting via Girsanov change of measure.
result URGE achieves better generation quality than existing methods.
This paper uses probability tensors for efficient path planning in complex scenarios.
problem Efficient path planning in complex environments with obstacles and multiple goals.
method Probability tensors are used to model agent motion and decision-making, incorporating past and future information.
result The model finds solutions in complex scenarios, demonstrating realistic emergent behaviors.
Two-dimensional transition rates improve life insurance reserve calculations.
problem Calculating life insurance reserves with Markov assumptions.
method Introducing two-dimensional forward and backward transition rates.
result Two-dimensional transition rates enable more accurate reserve calculations.
GH-PID uses guided harmonic paths for efficient SOT with interpretable diagnostics.
problem Efficiently solving Stochastic Optimal Transport with hard terminal distributions and soft costs.
method Guided Harmonic Path-Integral Diffusion (GH-PID) framework with low-dimensional guidance.
result GH-PID generates geometry-aware, cost-reducing trajectories that match terminal distributions.
We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for…
Auto-encoding is an important task which is typically realized by deep neural networks (DNNs) such as convolutional neural networks (CNN). In this paper, we propose EncoderForest (abbrv. eForest), the first tree ensemble based auto-encoder. We present a procedure for enabling forests to do backward reconstruction by ut…
New method infers hidden states in continuous-time phenomena better than traditional models.
problem Traditional HSMM's are limited to discrete time grids and cannot handle irregularly spaced data.
method Formulated integro-differential forward and backward equations for CTSMC's, introduced scalable Viterbi-type algorithm.
result Efficiently solved equations for posterior marginals and path estimates.
Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, …
Paper identifies reductive MDPs, solving them in polynomial time.
problem Computational hardness of general MDPs and tractability of finite-horizon MDPs.
method Defines reductivity, a new class of SSPs, and develops a polynomial-time solution.
result Optimal policies can be found in polynomial time for reductive SSPs and MDPs.
New method uses neural networks to solve complex PDEs from optimal control theory.
problem Solving high-dimensional Hamilton-Jacobi-Bellman PDEs.
method Iterative diffusion optimization techniques, focusing on path measures and divergences.
result Favourable properties of log-variance divergence for Monte Carlo estimators.
Method uses neural networks to solve combinatorial problems.
problem Solving combinatorial problems on raw input data.
method Integrates blackbox combinatorial solvers into neural networks.
result Efficient backward pass through blackbox solvers implemented.
Framework learns stochastic dynamics from endpoint and intermediate distributions using soft energy constraints.
problem Learning stochastic dynamics from endpoint and intermediate distributional observations.
method Formulates generation as a McKean-Vlasov control problem with soft energy constraints, solving it through FBSDE.
result Model learns coherent stochastic trajectories matching prescribed marginal laws.
A new method simplifies sampling from complex distributions without using diffusions.
problem Sampling from complex, high-dimensional distributions efficiently.
method Reduces sampling to solving a sequence of 'nice' sampling problems using SLC distributions.
result Shows how to traverse backwards paths using high-accuracy routines for SLC distributions.
We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static hedging arguments. This can be accomplished by taking various routes through some a…
We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence…
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
problem Nonlinear Forward Backward Stochastic Differential Equations (FBSDE) with terminal conditions.
method Backward deep BSDE method applied to FBSDE with nonlinear generators and random initial conditions.
result Derives exact and Taylor-based approximations for time-stepping nonlinear BSDEs.
Investigates time-inconsistent portfolio selection under MMV preferences.
problem Time-inconsistent optimal strategies for MMV preferences.
method Nash equilibrium controls for MMV and MV preferences, solving FBSDE and HJB equations.
result MMV optimal strategies lead to higher investment amounts than MV strategies, narrowing over time.
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a…
New method recovers BSDE from financial data without ergodicity.
problem Discovering probabilistic laws from financial data.
method Stochastic SINDy method under risk-neutral measure.
result Recovery of BSDE from limited financial data.
Paper presents a new insurance model equation for diverse structures.
problem Handling diverse insurance models with a single equation.
method Developed a canonical model construction and stochastic backward equations.
result Comparison theorems for different models follow from the new equation.
There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to ca…
Backward exploration reduces sample complexity in policy evaluation.
problem Empirical policy evaluation in reinforcement learning.
method Backward exploration algorithms from high-cost states.
result Reduced average-case sample complexity to O(logS). The study introduces backward baselines to distinguish past prediction from future prediction in machine learning models.
problem Differentiating between past and future prediction in machine learning models.
method Theoretical, empirical, and normative arguments support a family of simple and efficient statistical tests called backward baselines.
result The study provides a meaningful backward baseline for auditing black-box prediction systems.
The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids an…
Paper presents IMRCs for evolving tasks with forward and backward learning.
problem Incremental learning of evolving tasks with few samples per task.
method Incremental minimax risk classifiers (IMRCs) that exploit forward and backward learning.
result IMRCs provide significant performance improvement, especially with reduced sample sizes.