arXiv subjects

Hun O

Publications and source records attributed to Hun O.

4 recordsLinked to original sources

arXiv2019

A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration

In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard iteration but it differs on underlying Monte-Carlo sample generation and enables an improvement in the sense of complexity. We prove the explicit error estimates for the case where the generator does not depend on control variate.

math.NA↗

arXiv2019

Uniqueness, Comparison and Stability for Scalar BSDEs with {Lexp(\mu sqrt(2log(1+L)))}-integrable terminal values and monotonic generators

This paper considers a class of scalar backward stochastic differential equations (BSDEs) with $L\exp(\mu\sqrt{2\log(1+L)})$-integrable terminal values. We associate these BSDEs with BSDEs with integrable parameters through Girsanov change. Using this technique, we prove uniqueness, comparisons and stability for them under an extended monotonicity condition (more precisely one sided Osgood condition).

math.PR↗

arXiv2019

Stochastic Gronwall's inequality in random time horizon and its application to BSDE

In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under stochastic monotonicity condition.

math.PR↗

arXiv2018

A Framework of BSDEs with Stochastic Lipschtz Coefficients through Time Change

In this paper, we suggest a useful technique based on time change to be effective for dealing with the backward stochastic differential equations. We show the relation between the BSDEs with stochastic Lipschtz coeffecients and the ones with uniformly Lipschtz coefficients and stopping terminal time.

math.PR↗