Indifference Strategies and Viscosity Solutions in 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

6. The Markovian Case

The last proposition associates the indifference BSDE and thus ultimately the model’s unique indifference strategy and thus its worst-case optimal solution with a PDE.

While instructive, Proposition 37 is usually of little practical value, because PDE (13) can in most cases only be solved numerically and then one needs an a-priori argument why a classical solution to the PDE exists and why the numerical scheme employed converges to such a classical solution. In the following we therefore consider cases, in which a version of Proposition 37 still holds true, if v is only a viscosity solution to (13)

Note that in contrast to [19, 3], the driver f of our BSDE is not Lipschitz in y, but satisfies the prerequisites of Theorems 30 and 31. The following theorem ensures existence and uniqueness of solutions to the corresponding PDE in our setting (the proof can be found in Appendix C):