Bibliographic record
Abstract
In portfolio risk management, the main foci are to control the aggregate risk of the \nentire portfolio and to understand the contribution of each individual risk unit in the \nportfolio to the aggregate risk. When univariate risk measures are used to quantify the \nrisks associated with a portfolio, there is usually a lack of consideration of correlations \nbetween individual risk units and the aggregate risk and of dependence among these risks. \nFor this reason, multivariate risk measures defined by considering the joint distribution of \nrisk units in the portfolio are more desirable. In this thesis, we define new multivariate risk \nmeasures by minimizing multivariate loss functions subject to various. constraints. With \nthe proposed multivariate risk measures, we obtain risk measures for the entire portfolio \nand each individual risk unit in the portfolio at the same time. \nIn Chapter 2, we introduce a multivariate extension of Conditional Value-at-Risk \n(CVaR) based on a multivariate loss function associated with different risks related to \nportfolio risk management. We prove that the defined multivariate risk measure satisfies \nmany desirable properties such as positive homogeneity, translation invariance and subadditivity. \nThen, we provide numerical illustrations with multivariate normal distribution to \nshow the effects of the parameters in the model. After that, we also perform a comparison \nbetween our multivariate CVaR and other traditional univariate risk measures such as VaR \nand CVaR. \nIn Chapter 3, we define a multivariate risk measure for capital allocation purposes. \nUnlike most of the existing allocation principles that assume the total capital is exogenously \ngiven, we obtain the optimal total capital for the entire portfolio and the optimal capital \nallocation to all the individual risk units in the portfolio at the same time. In this chapter, \nwe first discuss our model with a two-level organization/portfolio structure. Then, we \nmove to a more complex three-level organization/portfolio structure. We find that many \nof the existing allocation principles can be seen as special or limiting cases of our model. \nIn addition, our model can explain those allocation principles as solutions to optimization \nproblems. Finally, we provide a numerical example for the two-level organization/portfolio \nstructure model with two different error functions. \nIn Chapter 4, we introduce a multivariate shortfall risk measure induced by cumulative \nprospect theory (CPT) and give the corresponding risk allocations under the multivariate \nshortfall risk measure. To obtain this risk measure, we make an extension of previously \nstudied univariate generalized shortfalls induced by CPT and incorporate the idea of systemic \nrisk. In this study, we discuss the properties of the risk measure and conditions for its existence and uniqueness. Also, we perform a simulation study and a comparison \nto a previously studied multivariate shortfall to show that our model can provide a more \nreasonable risk measure and allocation result.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".