## 06.05.2024 14:15 Alexander Merkel TU Berlin: LQG Control with Costly Information Acquisition

Abstract
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).

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## 03.06.2024 14:15 Lorenzo Schönleber (Collegio Carlo Alberto in Turin): Implied Impermanent Loss: A Cross-Sectional Analysis of Decentralized Liquidity Pools

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.

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