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A stochastic Fubini theorem: BSDE method.

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  • 1School of Mathematics and Statistics, Southwest University, Chongqing, 400715 China.

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Summary
This summary is machine-generated.

This study introduces a novel method for proving a stochastic Fubini theorem using backward stochastic differential equations (BSDEs). This approach establishes the well-posedness of specific BSDEs incorporating Itô integrals within their drift terms.

Keywords:
backward stochastic differential equationrandom jumpsstochastic Fubini theorem

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Area of Science:

  • Stochastic Analysis
  • Probability Theory
  • Mathematical Finance

Background:

  • Backward stochastic differential equations (BSDEs) are crucial tools in financial mathematics and stochastic analysis.
  • Existing techniques for stochastic Fubini theorems often involve complex analytical methods.
  • The well-posedness of BSDEs with Itô integrals in the drift term remains an active area of research.

Purpose of the Study:

  • To establish a new stochastic Fubini theorem.
  • To demonstrate the application of this theorem to a specific class of BSDEs.
  • To investigate the well-posedness of BSDEs with Itô integrals under a refined Lipschitz condition.

Main Methods:

  • Solving a specialized backward stochastic differential equation (BSDE).
  • Developing a novel technique distinct from existing methods for stochastic Fubini theorems.
  • Applying the proven theorem to analyze the well-posedness of BSDEs.

Main Results:

  • A novel proof of the stochastic Fubini theorem is presented.
  • The well-posedness of a class of BSDEs featuring Itô integrals in the drift term is obtained.
  • A subtle Lipschitz condition is identified as key for ensuring well-posedness.

Conclusions:

  • The proposed method offers a new perspective on stochastic Fubini theorems.
  • The findings contribute to a deeper understanding of BSDEs, particularly those with Itô integrals.
  • The study provides a rigorous framework for analyzing complex stochastic models.