Shortfall Risk Through Fenchel Duality

2018 ◽  
Author(s):  
Zhenyu Cui ◽  
Jun Deng
Keyword(s):  
Fenchel Duality ◽  
Shortfall Risk

Shortfall risk through Fenchel duality

2018 ◽  
Vol 05 (02) ◽  
pp. 1850019 ◽  
Author(s):  
Zhenyu Cui ◽  
Jun Deng
Keyword(s):  
Minimization Problem ◽  
Optimization Problem ◽  
Risk Measures ◽  
Fenchel Duality ◽  
Risk Minimization ◽  
Decomposition Approach ◽  
Shortfall Risk ◽  
Stochastic Optimization Problem ◽  
Duality Approach ◽  
Randomized Test

In this paper, we propose a Fenchel duality approach to study the minimization problem of the shortfall risk. We consider a general increasing and strictly convex loss function, which may be more general than the situation of convex risk measures usually assumed in the literature. We first translate the associated stochastic optimization problem to an equivalent static optimization problem, and then obtain the explicit structure of the optimal randomized test for both complete and incomplete markets. For the incomplete market case, to the best of our knowledge, we obtain for the first time the explicit randomized test, while previous literature only established the existence through the supermartingale optional decomposition approach. We also solve the shortfall risk minimization problem for an insider through the enlargement of filtrations approach.

A Note on the Link between Asymmetric Risk and Shortfall Risk

2008 ◽  
Author(s):  
Ba M. Chu
Keyword(s):  
Shortfall Risk

Preference robust models in multivariate utility-based shortfall risk minimization

2020 ◽  
pp. 1-41
Author(s):  
Yuan Zhang ◽  
Huifu Xu ◽  
Wei Wang
Keyword(s):  
Risk Minimization ◽  
Shortfall Risk

scholarly journals Efficient hedging: Cost versus shortfall risk

2000 ◽  
Vol 4 (2) ◽  
pp. 117-146 ◽  
Author(s):  
Hans Föllmer ◽  
Peter Leukert
Keyword(s):  
Shortfall Risk ◽  
Efficient Hedging

Generalized Shortfall Risk Measure Based on Insurance Premium

2021 ◽  
Author(s):  
Sainan Zhang ◽  
Huifu Xu
Keyword(s):  
Risk Measure ◽  
Insurance Premium ◽  
Shortfall Risk

Shortfall Risk Models When Information on Loss Function Is Incomplete

2022 ◽  
Author(s):  
Erick Delage ◽  
Shaoyan Guo ◽  
Huifu Xu
Keyword(s):  
Partial Information ◽  
Risk Measures ◽  
Risk Attitude ◽  
Optimal Decision ◽  
Convex Programs ◽  
Risk Models ◽  
Shortfall Risk ◽  
Robust Version ◽  
Subjective Judgement ◽  
Optimal Decision Making

Utility-based shortfall risk measures effectively captures a decision maker's risk attitude on tail losses. In this paper, we consider a situation where the decision maker's risk attitude toward tail losses is ambiguous and introduce a robust version of shortfall risk, which mitigates the risk arising from such ambiguity. Specifically, we use some available partial information or subjective judgement to construct a set of plausible utility-based shortfall risk measures and define a so-called preference robust shortfall risk as through the worst risk that can be measured in this (ambiguity) set. We then apply the robust shortfall risk paradigm to optimal decision-making problems and demonstrate how the latter can be reformulated as tractable convex programs when the underlying exogenous uncertainty is discretely distributed.

Optimal Portfolios Under Bounded Shortfall Risk and Partial Information

2007 ◽  
pp. 581-586 ◽  
Author(s):  
Ralf Wunderlich ◽  
Jörn Sass ◽  
Abdelali Gabih
Keyword(s):  
Partial Information ◽  
Optimal Portfolios ◽  
Shortfall Risk
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