Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Financial Market Model and Worst-Case Optimization Problem 2. Financial Market Model and Worst-Case Optimization Problem 3. Solution to the Post-Crash Problem 3. Solution to the Post-Crash Problem 4. Solution to the Pre-Crash Problem 4. Solution to the Pre-Crash Problem 5. A BSDE Characterization of Indifferences Strategies 5. A BSDE Characterization of Indifferences Strategies 6. The Markovian Case 6. The Markovian Case 7. Numerical Experiments 7. Numerical Experiments Acknowledgments and References Acknowledgments and References Appendix A. Proofs from Section 3 Appendix A. Proofs from Section 3 Appendix B. Proofs of BASDE Results from Section 5 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 Appendix B. Proofs of BSDE results from Section 5 Proof. (Proposition 27) In view of Subsection 5.1, the generator of the BSDE can be written as Proof Proof. (Theorem 28) We approximate the generator f by the functions Proof From this equation, we get by taking conditional expectations w.r.t. Ft and using Young’s inequality that for all q ∈ (0,∞ Further, (21) implies, together with Doob’s martingale inequality, Burkholder-Davis-Gundy’s, Young’s inequality and the fact that that there is a constant c, such that for all R ∈ (0,∞), where we used Young’s inequality again for the second estimate. Replacing the last term with the help of inequality (22), we arrive at Now, by dominated convergence we get that for t ∈ [0, T], Gronwall’s inequality now shows that for r ∈ [t, T]: The terms can be further estimated by Authors:
(1) Sascha Desmettre;
(2) Sebastian Merkel;
(3) Annalena Mickel;
(4) Alexander Steinicke. Authors: Authors: (1) Sascha Desmettre; (2) Sebastian Merkel; (3) Annalena Mickel; (4) Alexander Steinicke. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

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

Mastering LSEnet: Automated Graph Clustering in Lorentz Hyperbolic Space

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

2026 Graph Analytics & Financial Risk Modeling: LSEnet vs. Stochastic Crash Optimization

Smart Trading Under Fire: Portfolio Defense Against Market Crashes

Worst-Case Portfolio Optimization & Hyperbolic Graph Clustering

LSEnet & Market Defense: Hyperbolic AI and Crash-Proof Portfolios (2026)

Indifference Strategies and Viscosity Solutions in Worst-Case Portfolio Optimization

Bates and Heston Model Numerics: CIR Process Simulation and Infinite Activity Jumps

2026 Graph Analytics & Financial Risk Modeling: LSEnet vs. Stochastic Crash Optimization

Smart Trading Under Fire: Portfolio Defense Against Market Crashes

Worst-Case Portfolio Optimization & Hyperbolic Graph Clustering

LSEnet & Market Defense: Hyperbolic AI and Crash-Proof Portfolios (2026)

Indifference Strategies and Viscosity Solutions in Worst-Case Portfolio Optimization

Bates and Heston Model Numerics: CIR Process Simulation and Infinite Activity Jumps

Light-Mode

Classic

Newspaper

Minty

Dark-Mode

Neon Noir

Minty

HN StartUps