A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops a numerical scheme for solving path-dependent FBSDEs and PDEs.
Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
Deep signature algorithm for pricing path-dependent options.
(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backwa…
New method tackles convergence issues in approximating FBSDEs.
Deep learning method improves numerical approximation of FBSDEs with jumps.
A new scheme for FBSDEs simplifies computation without Monte Carlo.
Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
Extends deep solver to FBSDEs with jumps for option pricing.
Deep learning solves non-Markovian FBSDEs for utility maximization.
Study validates numerical method for singular FBSDEs convergence.
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into t…
We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to simila…
We analyze a market impact game between risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in t…
Study analyzes portfolio liquidation games influenced by self-exciting order flow.
Study how transaction costs impact stock returns and holdings in equilibrium.
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…
Study numerical methods for singular FBSDEs with degenerate forward component.
New deep learning method solves stochastic control problems.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
Extend classical theory of affine processes to path-dependent setting
The paper develops methods to price and hedge options in path-dependent stock models.
Study of a game with multiple players and common shocks using probabilistic methods.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we derive explicit expression f…
Dupire's functional Itô calculus provides an alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices. In this paper, we introduce a measure of path-dependence of functionals within the functional Itô calculus framework. Name…
The study examines insurance demand under rough volatility and path-dependent shocks.
New sampling method uses stochastic interpolants and FBSDEs.
In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FB…
Path-dependent PDEs model VIX and Realised Variance options.
In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an a…
In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approac…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local…
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…
Model strategic interactions between market makers and traders to optimize execution.
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent deriv…
The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.
Framework learns stochastic dynamics from endpoint and intermediate distributions using soft energy constraints.
Extends Itô's formula for path-dependent functions in finance.
New approach uses FBSDE to sample complex distributions.
We study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semilinear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions all…
PDGM uses neural nets to solve complex financial equations.
Study Nash equilibrium in market with relative wealth concerns under partial information and heterogeneous priors.
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 …