Advanced Risk Analytics: Hyperbolic Graph Clustering and Worst-Case Portfolio Optimization

Table of Links

Abstract and 1. Introduction

2. Financial Market Model and Worst-Case Optimization Problem

3. Solution to the Post-Crash Problem

4. Solution to the Pre-Crash Problem

5. A BSDE Characterization of Indifferences Strategies

6. The Markovian Case

7. Numerical Experiments

Acknowledgments and References

Appendix A. Proofs from Section 3

Appendix B. Proofs of BASDE Results from Section 5

Appendix C. Proofs of (CIR) Results from Section 6

Appendix C. Proofs of (CIR) results from Section 6

Proof. (Theorem 38) For bounded λ, σ we refer to [3, Theorem 3.5], since the conditions of the generator of the BSDE (8) are met.

As there is a K > 0 such that

(granted by assumption (14)) it follows by dominated convergence that

As a last step, to give a sufficient relation to use the proof of [3, Theorem 3.4], we have to bound the solution to the following BSDE:

From this point on, the proof can now be performed just as the one of [3, Theorem 3.4].