arXiv subjects

Hasib Uddin Molla

Publications and source records attributed to Hasib Uddin Molla.

4 recordsLinked to original sources

arXiv2026

A Policy Iteration Scheme for Semilinear Stochastic Hamilton-Jacobi-Bellman Equations with Exponential Convergence

This paper is concerned with the non-Markovian stochastic optimal control problems in which the value function is a random field characterized by a stochastic Hamilton-Jacobi-Bellman (SHJB) equation. When the stochastic integration coefficients are not controlled, the SHJB equation takes a semilinear form, which is subject to computational challenges compared to the Markovian case due to the measurable randomness. We introduce a policy-iteration algorithm based on successive linearization that reduces the nonlinear SHJB equation to a sequence of linear ones. Furthermore, we prove that the resulting approximation sequence converges monotonically to the value function in the mean-square sense with an exponential rate.

math.OC↗

arXiv2026

Generative Pricing of Basket Options via Signature-Conditioned Mixture Density Networks

We present a generative framework for pricing European-style basket options by learning the conditional terminal distribution of the log arithmetic-weighted basket return. A Mixture Density Network (MDN) maps time-varying market inputs encoded via truncated path signatures to the full terminal density in a single forward pass. Traditional approaches either impose restrictive assumptions or require costly re-simulation whenever inputs change, limiting real-time use. Trained on Monte Carlo (MC) under GBM with time-varying volatility or local volatility, the MDN acts as a reusable surrogate distribution: once trained, it prices new scenarios by integrating the learned density. Across maturities, correlations, and basket weights, the learned densities closely match MC (low KL) and produce small pricing errors, while enabling \emph{train-once, price-anywhere} reuse at inference-time latency.

q-fin.PR↗

arXiv2025

A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications

In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Markovian framework but also addresses fully coupled settings, in which both the drift and diffusion coefficients of the forward process may be random and depend on the backward components $Y$ and $Z$. Furthermore, we illustrate the practical applicability of our framework by addressing utility maximization problems under rough volatility, which are solved numerically with the proposed deep learning-based methods.

q-fin.MF↗

arXiv2020

Numerical Approximations of Coupled Forward-Backward SPDEs

We propose and study a scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled nonlinear forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. Precisely, we generalize the pioneering work of Dunst and Prohl [SIAM J. Sci. Comp., 38(2017), 2725--2755] by considering general nonlinear and nonlocal FBSPDEs with more inclusive coupling; self-contained proofs are provided and different numerical techniques for the resulting finite-dimensional equations are adopted. For such FBSPDEs, we first prove the existence and uniqueness of the strong solution as well as of the weak solution. Then the finite element method in the spatial domain leads to approximations of FBSPDEs by finite-dimensional forward-backward stochastic differential equations (FBSDEs) which are numerically computed by using some deep learning-based schemes. The convergence analysis is addressed for the spatial discretization of FBSPDEs, and the numerical examples, including both decoupled and coupled cases, indicate that our methods are quite efficient.

math.NA↗