Robust Portfolio Optimization with Respect to Spectral Risk Measures Under Correlation Uncertainty

Tsang, Man Yiu; Sit, Tony; Wong, Hoi Ying

doi:10.1007/s00245-022-09856-1

Cited by 3 publications

(1 citation statement)

References 52 publications

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“…The modeling and analysis of stochastic processes subject to ambiguities have long been studied in economics and other related fields, where the ambiguity is probabilistically measured by using the Radon–Nikodym derivative between the benchmark and distorted models (Anderson et al, 2003; Dowd et al, 2008). In these fields, many studies have applied risk measures to real‐world time series data (Imai, 2022; Tsang et al, 2022). The mathematical universality of model ambiguity is applicable to stochastic processes not only in economics but also in other research fields, including environmental management and restoration.…”

Section: Introductionmentioning

confidence: 99%

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

Yoshioka,

Yoshioka

2023

Environmetrics

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The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

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