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
2. Financial Market Model and Worst-Case Optimization Problem
A particularly important choice of those parameters leads to the following version of the Bates model [5] and Heston model [24], respectively:
In addition, we need the following integrability assumptions on the market coefficients λ and σ:
Admissible portfolio processes. We restrict our attention to admissible portfolio processes with continuous paths.
Note that the SDEs above are driven by the Brownian motion W with coefficients that are measurable w.r.t. a larger filtration than the one generated by W only.
The solution to the above SDE can then be given explicitly:
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Authors:
(1) Sascha Desmettre;
(2) Sebastian Merkel;
(3) Annalena Mickel;
(4) Alexander Steinicke.
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This paper is available on arxiv under CC BY 4.0 DEED license.
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[1] This means we rule out short sales of the risky asset.
