Optimal wealth strategy derived for jump-diffusion models with liabilities.
problem Maximizing utility in jump-diffusion models with random liabilities.
method Forward Backward SDEs system for optimal strategy.
result Explicit results for pure jump model and exponential utilities.
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…
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. …
New framework trains Schrödinger Bridge models using SDEs for generative tasks.
problem Unclear relation between SB optimization and modern generative model training.
method Forward-Backward SDEs theory for likelihood training of SB models.
result Training algorithm achieves comparable results on image generation datasets.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
Study on feature learning dynamics in infinite-depth neural networks, focusing on ResNets.
problem Understanding how features evolve during training in deep neural networks, especially in the large-depth limit.
method Conditional Gaussian representations and SDE system with decoupled backward weights.
result Depth-induced suppression of forward-backward coupling in infinite-depth networks, leading to a decoupled forward-backward SDE system.
This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit …
This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…
Model for multi-period carbon market pricing with allowances.
problem Carbon market pricing with multiple trading periods and compliance times.
method Singular forward-backward stochastic differential equations (SDEs).
result Value function convergence to infinite period model under certain conditions.
New method for efficient conditional sampling from diffusion models.
problem Efficient conditional simulation from diffusion models.
method Explicit forward-backward bridging to express conditional simulation as an inference problem.
result Principled particle Gibbs and pseudo-marginal samplers for conditional distribution.
Solves wealth maximization problem using variational analysis.
problem Maximizing expected utility of terminal wealth.
method Variational analysis, forward-backward stochastic differential equation (FBSDE).
result Characterization and solutions for various utility functions.
We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a {convergence} result of the solution…
We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial…
We propose a model for hedging in a market with jumps for a large investor. The dynamics of the stock prices and the value process is governed by forward-backward SDEs driven by Teugels martingales. Unlike known FBSDE market models, ours accounts for jumps in stock prices. Moreover, it allows to find an optimal hedging…
Optimal trading strategy adapts to signals in markets with price impact.
problem Optimal liquidation in markets with linear price impact and predictive signals.
method Formulated as a stochastic control problem, solved using probabilistic and convex analytic techniques.
result Explicit solution for optimal trading strategy in terms of SDEs.
Paper presents a new approach to a strategic insider equilibrium problem in continuous time.
problem Continuous time Kyle-Back model between insider and market marker.
method Uses forward-backward stochastic differential equations (FBSDEs) for characterization of equilibria.
result Characterizes all equilibria through FBSDEs and shows uniqueness of equilibrium without Markovian restrictions.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
DSB approximates SB problem for faster generative modeling.
problem Fast generation from complex data distributions.
method Entropy-regularized optimal transport on path spaces.
result DSB yields faster convergence to data distribution.
Study numerical methods for singular FBSDEs with degenerate forward component.
problem Numerical approximation of singular fully coupled FBSDEs with degenerate forward component and non-smooth terminal condition.
method Splitting approach to treat diffusion and transport parts separately.
result The splitting method converges with rate 1/2 under structural condition.
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of …
Investor optimizes utility in a market with endogenous pricing.
problem Maximizing utility in an incomplete market with endogenous pricing.
method Characterized optimality via FBSDEs and BSPDEs using generalized subgradients.
result Existence and smoothness of solutions for optimal investment and FBSDEs.
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 …
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.
Study optimal investment in large populations of competitive, heterogeneous agents.
problem Maximizing utility in a large, interacting agent system with relative performance concerns.
method Analyzes stochastic utility maximization game in finite and infinite agent settings, using graphon models and backward stochastic differential equations.
result Convergence of Nash equilibria and optimal utilities from finite to infinite agent models under specific conditions.
A new framework models uncertainty in structured temporal data using SDEs and neural networks.
problem Uncertainty quantification in machine learning applications involving structured and temporal data.
method Integrates stochastic differential equations (SDEs) with deep generative models in a variational autoencoder framework.
result Improves uncertainty quantification in machine learning applications involving structured and temporal data.
Study uses MFG approach to model equilibrium pricing with market clearing condition.
problem Continuous asset pricing with market clearing condition.
method Mean field game approach to solve forward-backward SDEs of McKean-Vlasov type.
result Net order flow converges to zero in large N-limit with specified conditions.
Backward SDEs help price XVA for OTC derivatives.
problem XVA valuation for OTC derivatives with default risk.
method Review and apply BSDEs with random horizon.
result Explicit formula for XVA correction terms.
Deep learning solves complex PA mean field games with market-clearing conditions.
problem Optimizing Principal-Agent interactions in renewable energy markets with market-clearing conditions.
method Actor-critic approach, deep backward stochastic differential equations (BSDE), neural net approximation.
result Efficacy of the deep learning algorithm in solving complex PA mean field games.
A new sampling method called Restart improves both speed and quality of generative processes.
problem Balancing speed and quality in generative processes involving differential equations.
method Alternates between adding noise and following ODE, improving both speed and quality.
result Surpasses previous SDE and ODE samplers in both speed and accuracy.
Study Nash equilibrium between broker and informed trader in dealer and lit markets.
problem Nash equilibrium between broker and informed trader in dealer and lit markets with partial information.
method Convex analysis, FBSDEs, polynomial approximation.
result Existence and uniqueness of Nash equilibrium for short time horizons.
We present a deep recurrent neural network architecture to solve a class of stochastic optimal control problems described by fully nonlinear Hamilton Jacobi Bellmanpartial differential equations. Such PDEs arise when one considers stochastic dynamics characterized by uncertainties that are additive and control multipli…
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.
Novel method for SDE calibration from sparse data using neural flows.
problem Calibrating SDEs from sparse, noisy observations.
method Characterization of posterior SDE using neural networks trained to solve a PDE with multiplicative updates.
result Significant improvement in scalability and accuracy compared to classical methods.
Deep model improves option pricing for CSI 300 index with sentiment and volatility features.
problem Challenges in real market option pricing, especially with constant volatility assumption.
method Deep Forward-Backward Stochastic Differential Equation (FBSDE) framework with dual-network architecture.
result Significant reduction in MAE and MAPE compared to BSM model.
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.
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.
New MFG model for MV portfolio management with peer-based risk aversion.
problem Time-inconsistent mean-variance portfolio management with peer-based risk aversion.
method Mean-field game, smooth regularization, fixed-point arguments, convergence analysis.
result Existence of mean-field equilibrium in time-inconsistent MFG.
SGD converges with perturbed forward-backward passes, explained by geometric amplification.
problem Analyzing convergence of SGD with perturbed forward-backward passes in composite optimization.
method Characterized propagation and amplification of perturbations, derived convergence guarantees for non-convex and PL objectives.
result Perturbations cascade through the computational graph, affecting convergence order under specific conditions.
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
New model solves complex SDEs with high-dimensional spatial and stochastic spaces.
problem Solving SDEs with high-dimensional spatial and stochastic spaces.
method Physics-informed deep generative model (sPI-GeM) combining PI-BasisNet and PI-GeM.
result Scalable solution for high-dimensional SDE problems.
In this paper, we further study the forward-backward envelope first introduced in [28] and [30] for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the origin…
New method for dynamic valuation in markets with random endowments.
problem Dynamic valuation in markets with random endowments.
method Developed new FBSDE systems and established optimality conditions.
result Established necessary and sufficient conditions for optimality.
Proximal Diffusion Models improve generative model efficiency.
problem Improving generative model efficiency and accuracy.
method Developed Proximal Diffusion Models using proximal maps instead of scores.
result Proximal Diffusion Models achieve faster convergence and higher accuracy.
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…
Efficiently trains forward processes to minimize generative trajectories curvature.
problem High curvature of generative trajectories slows down sampling speed.
method Trains forward process to minimize curvature without ODE/SDE simulation.
result Lower curvature than previous models, decreased sampling costs.
Extends SABR model for pricing RFR caplets.
problem Pricing backward RFR caplets in a post-Libor market.
method Closed-form effective SABR parameters for backward RFR caplets.
result Closed-form solution for backward RFR caplets.
Neural network models accurately price assets in rough Bergomi model.
problem Accurately pricing assets in the rough Bergomi model with hidden parameters.
method Used a neural SDE to learn the forward variance curve, proposing a numerical scheme for simulation.
result The learned forward variance curve calibrates asset prices and option prices simultaneously.
DeepGSB solves MFGs with non-differentiable preferences.
problem Solving MFGs with non-differentiable preferences and exact population convergence.
method Generalized Schrödinger Bridge via Forward-Backward SDEs and Temporal Difference learning.
result DeepGSB provides necessary and sufficient conditions for mean-field problems.