A Class of Multi-dimensional Backward Stochastic Differential Equations with Singular Generators exhibiting Diagonally Quadratic Growth and Applications

TL;DR

This paper studies a new class of multi-dimensional BSDEs with singular, diagonally quadratic generators and unbounded terminal conditions, extending existing results and demonstrating applications in optimal investment decisions.

Contribution

It introduces a novel class of BSDEs with singular generators and diagonally quadratic growth, expanding theoretical understanding and practical applications.

Findings

Extended the theory of BSDEs to include singular, diagonally quadratic generators.

Provided an example demonstrating application in optimal investment.

Generalized existing results to unbounded terminal conditions.

Abstract

This paper investigate a class of multi-dimensional backward stochastic differential equations (BSDEs) with singualr generators exhibiting diagonally quadratic growth and unbounded terminal conditions, thereby extending results in the literature. We present an example of such equations in optimal investment decision.