A new approach to managing counterparty credit risk using BSDEs.
problem Managing counterparty credit risk in financial markets.
method Dynamic replication approach and fundamental BSDE for credit risk modeling.
result A reduced fundamental BSDE solution for explicit or approximate representation of credit risk adjusted portfolio value.
Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.
problem Optimal consumption-investment problem with recursive utility.
method Established connection to quadratic BSDE, derived stochastic maximum principle.
result Proved existence of optimal strategy and analyzed coupled system.
Deep learning method uses asymptotic expansion to solve high-dimensional BSDEs faster.
problem Solving high-dimensional BSDEs efficiently.
method Asymptotic expansion as prior knowledge in deep learning for BSDEs.
result Significantly reduces loss function and accelerates convergence.
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
problem Long-term decomposition of robust pricing kernels under G-expectation.
method Proposes and analyzes three types of quadratic G-BSDEs to decompose pricing kernels.
result Pricing kernels decomposed into four components: discounting, transitory, symmetric martingale, and volatility uncertainty.
The paper tackles pricing vulnerable options via generalized BSDEs and penalization schemes.
problem Pricing options in a general hazard process setup.
method Establishes well-posedness and comparison theorems for generalized BSDEs and RBSDEs, studies penalization schemes.
result Well-posedness results and comparison theorems for generalized BSDEs and RBSDEs, extended penalization schemes.
Develops geometric BSDEs for modeling dynamic return risk measures.
problem Modeling continuous-time dynamic return risk measures.
method Introduces and develops Geometric Backward Stochastic Differential Equations (GBSDEs) and two-driver BSDEs.
result Establishes existence, regularity, uniqueness, and stability of solutions to GBSDEs.
New methods solve complex financial equations.
problem Solving backward stochastic differential equations driven by continuous-time Markov chains.
method Multi-stage Euler-Maruyama methods and multilevel spatial discretization.
result Efficiently solved stiff Markov BSDEs.
Study on BSDEs with random time horizon, focusing on existence and properties.
problem Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
method Method of reduction and examination of BSDEs with lahdlaug driver.
result Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
The paper represents performance processes in incomplete markets using BSDE.
problem Incomplete markets with stochastic factors.
method Ergodic and infinite horizon BSDEs for homothetic forward performance processes.
result Derivation of representations for power, exponential, and logarithmic forward performance processes.
The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
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.
Solves new quadratic BSDE systems for market performance analysis.
problem Characterizing forward performance processes in regime switching markets.
method Introduces and solves ergodic BSDE systems in infinite time horizon.
result Connection between ergodic BSDE solutions and long-term growth rates of utility maximization.
The paper studies BSDEs and their densities in biology and finance.
problem Existence of densities for solutions of BSDEs.
method Conditions for Malliavin differentiability and application to gene expression and finance.
result Results on existence of densities for BSDEs solutions.
This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equation…
Study forward entropic risk measures using BSDEs, showing convergence and comparing with classical measures.
problem Understanding the behavior of forward entropic risk measures over long maturities.
method Utilized ergodic BSDEs to represent and analyze forward entropic risk measures.
result Forward entropic risk measures converge to a constant exponentially fast for long maturities.
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.
BSDEs help in financial pricing and utility maximization.
problem Financial pricing and utility maximization in complex market models.
method Introduces and applies BSDEs to financial problems.
result Utilizes BSDEs for simple utility maximization solutions.
KANHedge improves hedging of high-dimensional options using learnable B-spline activation functions.
problem Challenges in high-dimensional option pricing and hedging due to the curse of dimensionality.
method Introduces KANHedge, a novel BSDE-based hedger leveraging Kolmogorov-Arnold Networks with learnable B-spline activation functions.
result KANHedge provides improved hedging performance, achieving significant reductions in hedging cost metrics.
Study solves BSDEs for bond market hedging, proving convergence of strategies.
problem Approximate hedging in bond markets using BSDEs.
method Existence and uniqueness of solutions for infinite-dimensional BSDEs driven by cylindrical martingales.
result Sequence of locally risk-minimizing strategies converges to generalized hedging strategy.
We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus part…
We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle L and the upper obstacle U of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by pasting local solutions and…
Extends stability approach to BSDEs with jumps, providing criteria for existence and uniqueness.
problem Existence and uniqueness of solutions to BSDEs with jumps.
method Monotone stability approach, non-convex generator, non-global Lipschitz conditions.
result Concrete criteria for existence and uniqueness of solutions, comparison, and bounds.
Paper introduces a new method to solve complex PDEs efficiently.
problem Solving high-dimensional semilinear PDEs and BSDEs.
method Decomposes PDEs into linear and nonlinear parts, uses Deep BSDE solver with control variate method.
result Errors of the new method are much smaller than those of the original Deep BSDE solver.
A new deep generative model uses BSDEs for high-dimensional data generation.
problem Generating high-dimensional complex data, especially images.
method Combines BSDEs with deep neural networks for training with MMD loss.
result BSDE-Gen effectively generates high-dimensional data with stochasticity.
Study approximates BSDEs with constraints using machine learning.
problem Approximating BSDEs with a constraint on the gains process.
method Discretization followed by machine learning approximation of the discretely constrained BSDE.
result The discretely constrained BSDE converges to the continuously constrained one as the mesh grid approaches zero.
A new method solves complex financial problems using deep learning.
problem Optimal stopping and option pricing in finance.
method Compound BSDE method, based on reformulating BSDEs.
result The method offers accurate and efficient solutions for high-dimensional problems.
Study uses BSDEs to price European options in markets with multiple defaults.
problem Pricing European options in markets with multiple defaultable assets.
method Non-linear Backward Stochastic Differential Equations (BSDEs) with multiple default jumps.
result Derives explicit formulas for option pricing in markets with multiple defaultable assets.
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
problem Analyzing convergence rates of BSDEs driven by Lévy processes.
method Approximating Lévy processes by compound Poisson processes and studying BSDEs.
result Optimal convergence rates derived for BSDEs in L2-norm and Wasserstein distance. Investment and insurance strategy optimized under inflation using BSDEs.
problem Optimal investment, consumption, and insurance selection in inflationary environment.
method Theory of quadratic-exponential backward stochastic differential equations (BSDEs) with jumps.
result Explicit solutions for optimal investment strategies under exponential and power utilities.
This paper optimizes credit portfolios considering contagion risk and partial information.
problem Optimizing credit portfolios in a market with contagion risk and partial information.
method Formulated a stochastic control problem under partial observations, connected to a quadratic BSDE with jumps.
result Existence and uniqueness of solution to the BSDE, leading to optimization results.
Novel filter uses deep BSDE for nonlinear density approximation.
problem Nonlinear filtering problem.
method Bayesian filter based on deep BSDE and neural networks.
result Theoretical convergence rate confirmed in numerical examples.
In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American o…
Study optimal liquidation strategies with infinite horizon and regime switching.
problem Optimal liquidation with semimartingale strategies in a stochastic environment.
method Characterization of value function and optimal strategy via BSDEs with infinite horizon.
result Existence and uniqueness of optimal control problem solutions.
Deep learning solves PDEs with boundary conditions for barrier options.
problem Solving PDEs with boundary conditions for barrier options.
method Employing deep learning to approximate solutions of the PDE with boundary conditions.
result Deep learning can solve PDEs with boundary conditions for barrier options.
The paper proves unique solutions for complex stochastic equations.
problem Stochastic equations with unbounded time horizons and jumps.
method Introduced a wellposedness result for multidimensional BSDEs with general martingales.
result Unique solutions for stochastic equations with unbounded time horizons and jumps.
New integration method improves BSDE-based PDE solvers.
problem Discretization bias in standard BSDE-based solvers.
method Proposed Stratonovich-based BSDE formulation with stochastic Heun integration.
result Eliminates bias issues and outperforms EM-based variants.
A new method uses BSDEs to solve optimal reinsurance under partial information.
problem Maximizing wealth in insurance with partial loss information.
method Backward Stochastic Differential Equations (BSDEs) for infinite-dimensional filtering problem.
result Optimal reinsurance strategy found via BSDE solution.
Study new BSDEs with mean reflection constraints.
problem Imposing mean reflection constraints on BSDE solutions.
method Introduced and analyzed new type of BSDEs with mean reflection constraints, proving well-posedness under natural Skorokhod condition.
result Extended results to include static risk measures, providing applications in super hedging.
New method decomposes submartingale systems for BSDEs with weak constraints.
problem Tackles decomposition of submartingale systems for BSDEs with weak constraints.
method Introduces Yg,ξ-submartingale systems and proves a Mertens decomposition using an original approach. result Proves a Mertens decomposition for Yg,ξ-submartingale systems. In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximiza…
New algorithm solves complex equations using deep learning.
problem High-dimensional nonlinear PDEs and BSDEs.
method Iterated time discretization, deep neural networks, stochastic gradient descent.
result Increased accuracy and reduced complexity compared to existing methods.
The paper provides a representation for dynamic risk measures and capital allocations.
problem Representation of dynamic risk measures and capital allocations under Itô-Lévy model.
method Representation theorem for dynamic capital allocation derived from BSDEs with quadratic-exponential growth.
result Derivation of a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.
Quantum Transformer solves high-dimensional PDEs with improved accuracy.
problem Solving high-dimensional parabolic PDEs in engineering and physics.
method Quantum Transformer BSDE solver using FC-VQC with causal attention.
result Quantum Transformer consistently outperforms classical methods on PDE benchmarks.
Investigates quadratic-exponential growth BSDEs with jumps and proves existence and differentiability.
problem Existence and differentiability of solutions to quadratic-exponential growth BSDEs with jumps.
method Proves existence and differentiability of solutions under general quadratic-exponential structure using local Lipschitz continuity and A_gamma-condition.
result Proves existence and differentiability of solutions under general quadratic-exponential structure.
This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or ac…
Study optimal liquidation with multiple regimes using BSDEs with singular terminal values.
problem Optimal liquidation with regime switching in dark pools.
method Introduced a system of BSDEs with jumps and singular terminal values.
result Existence and uniqueness results for the BSDE system are obtained.
Deep BSDE method for pricing and hedging complex financial portfolios.
problem Simultaneous pricing and delta-gamma hedging of large portfolios of multi-asset Bermudan options.
method Discretely reflected BSDEs, One Step Malliavin scheme, neural network regression Monte Carlo method.
result Efficient and accurate pricing and hedging strategies for high-dimensional portfolios.
Study game options pricing in nonlinear markets, extending previous work.
problem Pricing game options in nonlinear markets without arbitrage.
method Detailed study of unilateral pricing, hedging, and exercising problems using BSDE approach.
result Explicit results obtained under suitable assumptions about solutions to BSDEs.