# Asymptotic approach for backward stochastic differential equation with singular terminal condition *

## TL;DR

This paper establishes a detailed asymptotic analysis of solutions to backward stochastic differential equations with singular terminal conditions, linking them to solutions with singular generators and broadening uniqueness results.

## Contribution

It introduces a novel correspondence between solutions of BSDEs with singular terminal conditions and those with singular generators, enhancing understanding of their asymptotic behavior.

## Key findings

- Provides a precise asymptotic description of BSDE solutions near the terminal time.
- Extends the uniqueness of solutions to a broader class of generators.
- Establishes a one-to-one correspondence between two types of BSDE solutions.

## Abstract

In this paper, we provide a one-to-one correspondence between the solution Y of a BSDE with singular terminal condition and the solution H of a BSDE with singular generator. This result provides the precise asymptotic behavior of Y close to the final time and enlarges the uniqueness result to a wider class of generators.