Sample average approximation of CVaR-based hedging problem with a deep-learning solution

Cheng Peng, Shuang Li, Yanlong Zhao and Ying Bao

The North American Journal of Economics and Finance, 2021, vol. 56, issue C

Abstract: Conditional Value-at-Risk (CVaR) is an extremely popular risk measure in finance and is usually optimized to reduce the risk of large losses. This paper considers the CVaR optimization problem for hedging a portfolio of derivatives with bounded constraints. We focus on minimizing the CVaR of the loss of the hedging portfolio by a deep learning solution because of its promising application to classic portfolio optimization. As the cost objective function in the deep learning framework, the CVaR does not have a closed-form expression, but it can be estimated by using the i.i.d samples average approximation method. While many works have adopted minimizing the estimated CVaR to obtain the optimal solution, they lack theoretical performance guarantees for sample-based solutions. This paper attempts to bridge this gap. On the one hand, we introduce a typical deep neural network architecture for training the optimal hedging strategies, which helps us to analyze the properties of function set for this neural network. On the other hand, we offer a sufficient condition to guarantee that the optimal strategies obtained by using the estimated CVaR can be assured in practical applications. In particular, we prove that the uniform convergence in probability of the estimated CVaR to CVaR over a set of functions, which are generated by the proposed deep neural network. Numerical experiments verify the proposed sufficient condition and demonstrate the feasibility and superiority of this approach.

Keywords: Conditional Value-at-Risk; Hedging strategies; Deep learning; Theoretical guarantee; Sample average approximation; Uniform convergence (search for similar items in EconPapers)
JEL-codes: C5 C6 G1 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:56:y:2021:i:c:s1062940820302102

DOI: 10.1016/j.najef.2020.101325

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