Oberseminar Finanz- und Versicherungsmathematik

Jointly organised by Prof. Dr. Francesca Biagini, Prof. Dr. Thilo Meyer-Brandis, Prof. Dr. Christoph Knochenhauer, Prof. Dr. Aleksey Min, Prof. Dr. Matthias Scherer and Prof. Dr. Rudi Zagst


At LMU Mathematics Institute, Theresienstraße 39-B (Room B 349)
(how to find us).


6 May14:15 - 15:00Alexander Merkel,
Technical University of Berlin
LQG Control with Costly
Information Acquisition
3 June14:15 - 15:00

15:00 - 15:45
Lorenzo Schönleber,
Collegio Carlo Alberto in Turin

Maximilian Würschmidt,
University of Trier
Implied Impermanent Loss:
A Cross-Sectional Analysis
of Decentralized Liquidity


Titles and Abstracts

We consider the fundamental problem of Linear Quadratic Gaussian Control on an infinite horizon with costly information acquisition. Specifically, we consider a two-dimensional coupled system, where one of the two states is observable, and the other is not. Additionally, to inference from the observable state, costly information is available via an additional, controlled observation process.
Mathematically, the Kalman-Bucy filter is used to Markovianize the problem. Using an ansatz, the problem is then reduced to one of the control-dependent, conditional variance for which we show regularity of the value function. Using this regularity for the reduced problem together with the ansatz to solve the problem by dynamic programming and verification and construct the unique optimal control.
We analyze the optimal control, the optimally controlled state and the value function and compare various properties to the literature of problems with costly information acquisition. Further, we show existence and uniqueness of an equilibrium for the controlled, conditional variance, and study sensitivity of the control problem at the equilibrium.
At last, we compare the problem to the case of no costly information acquisition and fully observable states.
Joint work with Christoph Knochenhauer and Yufei Zhang (Imperial College London).

We propose a continuous-time stochastic model to analyze the dynamics of impermanent loss in liquidity pools in decentralized finance (DeFi) protocols. We replicate the impermanent loss using option portfolios for the individual tokens. We estimate the risk-neutral joint distribution of the tokens by minimizing the Hansen–Jagannathan bound, which we then use for the valuation of options on relative prices and for the calculation of implied correlations. In our analyses, we investigate implied volatilities and implied correlations as possible drivers of the impermanent loss and show that they explain the cross-sectional returns of liquidity pools. We test our hypothesis on options data from a major centralized derivative exchange.