Mastering LSEnet: Automated Graph Clustering in Lorentz Hyperbolic Space

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 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. (Theorem 28) We approximate the generator f by the functions

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