تقرير
Law-Invariant Return and Star-Shaped Risk Measures
| العنوان: | Law-Invariant Return and Star-Shaped Risk Measures |
|---|---|
| المؤلفون: | Laeven, Roger J. A., Gianin, Emanuela Rosazza, Zullino, Marco |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Quantitative Finance |
| مصطلحات موضوعية: | Quantitative Finance - Risk Management, Mathematics - Probability, Primary: 91B06, 91B30, 60E15, Secondary: 60H30, 62P05 |
| الوصف: | This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.19552 |
| رقم الأكسشن: | edsarx.2310.19552 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |