Coherent Risk Measures and Normal Mixture Distributions with Applications in Portfolio Optimization

2021 ◽  
Author(s):  
Xiang Shi ◽  
Young Shin Kim
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Mixture Distributions ◽  
Coherent Risk Measures ◽  
Normal Mixture ◽  
Coherent Risk

INSTABILITY OF PORTFOLIO OPTIMIZATION UNDER COHERENT RISK MEASURES

2010 ◽  
Vol 13 (03) ◽  
pp. 425-437 ◽  
Author(s):  
IMRE KONDOR ◽  
ISTVÁN VARGA-HASZONITS
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Optimal Portfolio ◽  
The Other ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Large Samples

It is shown that the axioms for coherent risk measures imply that whenever there is a pair of portfolios such that one of them dominates the other in a given sample (which happens with finite probability even for large samples), then there is no optimal portfolio under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered in the special example of Expected Shortfall which is used here both as an illustration and as a springboard for generalization.

scholarly journals LIQUIDITY RISK AND INSTABILITIES IN PORTFOLIO OPTIMIZATION

2016 ◽  
Vol 19 (05) ◽  
pp. 1650035 ◽  
Author(s):  
FABIO CACCIOLI ◽  
IMRE KONDOR ◽  
MATTEO MARSILI ◽  
SUSANNE STILL
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Risk Measure ◽  
Estimation Error ◽  
Coherent Risk Measures ◽  
Important Special Case ◽  
Coherent Risk ◽  
Finite Samples ◽  
Impact Function ◽  
The Impact

We show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures on finite samples. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show here that the impact function determines which regularizer is to be used. We also show that any regularizer based on the norm [Formula: see text] with [Formula: see text] makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with [Formula: see text] do not. The [Formula: see text] norm represents a border case: its “soft” implementation does not remove the instability, but rather shifts its locus, whereas its “hard” implementation (including hard limits or a ban on short selling) eliminates it. We demonstrate these effects on the important special case of expected shortfall (ES) which has recently become the global regulatory market risk measure.

scholarly journals Portfolio optimization with two coherent risk measures

2020 ◽  
Vol 78 (3) ◽  
pp. 597-626
Author(s):  
Tahsin Deniz Aktürk ◽  
Çağın Ararat
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Coherent Risk Measures ◽  
Coherent Risk
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