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Robust control problems of BSDEs coupled with value functions

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  • Zhou Yang
  • Jing Zhang
  • Chao Zhou

Abstract

A robust control problem is considered in this paper, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and their coefficients satisfy non-Lipschitz continuous and non-linear growth conditions, the objective function is expressed as a backward stochastic differential equation (BSDE) with the generator depending on the value function. We establish the existence and uniqueness of the value function in a proper space and provide a verification theorem. Moreover, we apply the results to solve two typical optimal investment problems in the market with ambiguity, one of which is with Heston stochastic volatility model. In particular, we establish some sharp estimations for Heston model with ambiguity parameters.

Suggested Citation

  • Zhou Yang & Jing Zhang & Chao Zhou, 2022. "Robust control problems of BSDEs coupled with value functions," Papers 2208.10735, arXiv.org.
    • Handle: RePEc:arx:papers:2208.10735
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    References listed on IDEAS

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