47 citations · 89 across the 8 of their papers we have counts for
10 papers
Minimizing Benchmark-Relative Drawdown Duration via Occupation Time Penalization
Jun Sekine, Marcus Wunsch
We study a continuous-time portfolio optimization problem in which an investor is evaluated relative to a non-replicable benchmark and seeks to control the persistence of benchmark…
Model-free Hedging of Impermanent Loss in Geometric Mean Market Makers
Masaaki Fukasawa, Basile Maire, Marcus Wunsch
We consider Geometric Mean Market Makers -- a special type of Decentralized Exchange -- with two types of users: liquidity takers and arbitrageurs. Liquidity takers trade at prices…
Deep Partial Hedging
Songyan Hou, Thomas Krabichler, Marcus Wunsch
Using techniques from deep learning (cf. [Büh+19]), we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in t…
Hedging Goals
Thomas Krabichler, Marcus Wunsch
Goal-based investing is concerned with reaching a monetary investment goal by a given finite deadline, which differs from mean-variance optimization in modern portfolio theory. In…
On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov equations
Jonatan Lenells, Marcus Wunsch
We show that the weakly dissipative Camassa-Holm, Degasperis-Procesi, Hunter-Saxton, and Novikov equations can be reduced to their non-dissipative versions by means of an exponenti…
The Hunter-Saxton system and the geodesics on a pseudosphere
Jonatan Lenells, Marcus Wunsch
We show that the two-component Hunter-Saxton system with negative coupling constant describes the geodesic flow on an infinite-dimensional pseudosphere. This approach yields explic…
Weak geodesic flow on a semi-direct product and global solutions to the periodic Hunter-Saxton system
Marcus Wunsch
We give explicit solutions to the two-component Hunter-Saxton system on the unit circle. Moreover, we show how global weak solutions can be naturally constructed using the geometri…
The geometry of a vorticity model equation
Joachim Escher, Boris Kolev, Marcus Wunsch
We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup…
Global existence for the generalized two-component Hunter-Saxton system
Hao Wu, Marcus Wunsch
We study the global existence of solutions to a two-component generalized Hunter-Saxton system in the periodic setting. We first prove a persistence result of the solutions. Then f…
Restrictions on the geometry of the periodic vorticity equation
Joachim Escher, Marcus Wunsch
We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group of all smooth and orientatio…