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<p>Motivated by Arai et al. Insur Math Econ 85:115-125. (2019), this paper introduces the novel concept of the generalized optimal initial capital (GOIC), which is induced by the generalized optimized certainty equivalent (GOCE) in the rank-dependent expected utility (RDEU) model. Building upon the comprehensive study of GOCE by Wu et al. SIAM J Finan Math , 15(1):255-294. (2024), we investigate the properties of GOIC with various types of loss functions. It is demonstrated that GOIC not only extends the utility-based shortfall risk measure but can also be shown to be a convex risk measure under specific conditions. We examine the conditions of the loss and distortion functions in relation to the coherence of both GOCE and GOIC. The study concludes with an exploration of the properties of risk measures generated by the generalized certainty equivalent.</p>

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Generalized Optimal Initial Capital and Risk Measures Induced by the Generalized Certainty Equivalent

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Zhenfeng Zou

摘要

Motivated by Arai et al. Insur Math Econ 85:115-125. (2019), this paper introduces the novel concept of the generalized optimal initial capital (GOIC), which is induced by the generalized optimized certainty equivalent (GOCE) in the rank-dependent expected utility (RDEU) model. Building upon the comprehensive study of GOCE by Wu et al. SIAM J Finan Math , 15(1):255-294. (2024), we investigate the properties of GOIC with various types of loss functions. It is demonstrated that GOIC not only extends the utility-based shortfall risk measure but can also be shown to be a convex risk measure under specific conditions. We examine the conditions of the loss and distortion functions in relation to the coherence of both GOCE and GOIC. The study concludes with an exploration of the properties of risk measures generated by the generalized certainty equivalent.