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Comparison theorems for some backward stochastic Volterra integral equations

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  • Wang, Tianxiao
  • Yong, Jiongmin

Abstract

For some backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison theorems for (forward) stochastic differential equations, backward stochastic differential equations, and (forward) stochastic Volterra integral equations (FSVIEs) are also presented. Duality principles are used in some relevant proofs. Also, it is found that certain kinds of monotonicity conditions play crucial roles to guarantee the comparison theorems for FSVIEs and BSVIEs to be true. Various counterexamples show that the assumed conditions are almost necessary in some sense.

Suggested Citation

  • Wang, Tianxiao & Yong, Jiongmin, 2015. "Comparison theorems for some backward stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1756-1798.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:1756-1798
    DOI: 10.1016/j.spa.2014.11.013
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    References listed on IDEAS

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    1. Beissner, Patrick & Rosazza Gianin, Emanuela, 2018. "The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time," Rationality and Competition Discussion Paper Series 72, CRC TRR 190 Rationality and Competition.
    2. Wang, Tianxiao & Yong, Jiongmin, 2019. "Backward stochastic Volterra integral equations—Representation of adapted solutions," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4926-4964.

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