تقرير
Dynamic Return and Star-Shaped Risk Measures via BSDEs
| العنوان: | Dynamic Return and Star-Shaped Risk Measures via BSDEs |
|---|---|
| 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: 60H10, 91B06, Secondary: 60H30, 62P05 |
| الوصف: | This paper establishes characterization results for dynamic return and star-shaped risk measures induced via backward stochastic differential equations (BSDEs). We first characterize a general family of static star-shaped functionals in a locally convex Fr\'echet lattice. Next, employing the Pasch-Hausdorff envelope, we build a suitable family of convex drivers of BSDEs inducing a corresponding family of dynamic convex risk measures of which the dynamic return and star-shaped risk measures emerge as the essential minimum. Furthermore, we prove that if the set of star-shaped supersolutions of a BSDE is not empty, then there exists, for each terminal condition, at least one convex BSDE with a non-empty set of supersolutions, yielding the minimal star-shaped supersolution. We illustrate our theoretical results in a few examples and demonstrate their usefulness in two applications, to capital allocation and portfolio choice. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.03447 |
| رقم الأكسشن: | edsarx.2307.03447 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |