English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the issue of solution uniqueness for portfolio optimizationproblem and its inverse for asset returns with a finite number of possiblescenarios. The risk is assessed by deviation measures introduced by[Rockafellar et al., Mathematical Programming, Ser. B, 108 (2006), pp. 515-540]instead of variance as in the Markowitz optimization problem. We prove that ingeneral one can expect uniqueness neither in forward nor in inverse problems.We discuss consequences of that non-uniqueness for several problems in riskanalysis and portfolio optimization, including capital allocation, risksharing, cooperative investment, and the Black-Litterman methodology. In allcases, the issue with non-uniqueness is closely related to the fact thatsubgradient of a convex function is non-unique at the points ofnon-differentiability. We suggest methodology to resolve this issue byidentifying a unique "special" subgradient satisfying some natural axioms. This"special" subgradient happens to be the Stainer point of the subdifferentialset.

On the solution uniqueness in portfolio optimization and risk analysis