arXiv subjects

Jiuk Jang

Publications and source records attributed to Jiuk Jang.

2 recordsLinked to original sources

arXiv2023

A discretization scheme for path-dependent FBSDEs and PDEs

This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key contribution of our approach is a novel estimator for the martingale integrand in the FBSDE, specifically designed to handle path-dependence more reliably than existing methods. We derive a concentration inequality that quantifies the statistical error of this estimator in a Monte Carlo framework. Based on these results, we investigate a supervised learning method with neural networks for solving path-dependent PDEs. The proposed algorithm is fully implementable and adaptable to a broad class of path-dependent problems.

math.PR↗

arXiv2019

Hedging short-maturity Asian options in local volatility models

This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a H\"older continuous payoff function in a local volatility model. The main idea of this analysis is that the local volatility model can be approximated by a Gaussian process at short maturity. By combining this approximation argument with Malliavin calculus, we derive short-maturity asymptotics for Asian option prices and deltas, and express them in terms of the local volatility function and the initial stock price. In addition, we show that the convergence rate of the approximation is determined by the H\"older exponent of the payoff function. Numerical experiments on concrete examples validate the effectiveness of the proposed method.

q-fin.MF↗