# 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

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).

Dates | Times | Speakers | Titles |
---|---|---|---|

6 May | 14:15 - 15:00 | Alexander Merkel, Technical University of Berlin | LQG Control with Costly Information Acquisition |

3 June | 14:15 - 15:00 15:00 - 15:45 16:15 - 17:00 | Lorenzo Schönleber, Collegio Carlo Alberto, University of Turin Maximilian Würschmidt, University of Trier Marco Frittelli, University of Milan | Implied Impermanent Loss: A Cross-Sectional Analysis of Decentralized Liquidity Pools A Probabilistic Approach to Shape Derivatives Collective Arbitrage, Super-replication and Risk Measures |

1 July | 14:15 - 15:00 | Michael Kupper, University of Konstanz | Discrete approximation of risk-based pricing under volatility uncertainty |

15 July | 14:15 - 15:00 | Xunyu Zhou, Columbia University | Reinforcement Learning for Diffusion Processes |

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).

The theory we present aims at expanding the classical Arbitrage Pricing Theory to a setting where N agents invest in stochastic security markets while also engaging in zero-sum risk exchange mechanisms.

We introduce in this setting the notions of Collective Arbitrage and of Collective Super-replication and accordingly establish versions of the fundamental theorem of asset pricing and of the pricing-hedging duality.

When computing the Collective Super-replication price for a given vector of contingent claims, one for each agent in the system, allowing additional exchanges among the agents reduces the overall cost compared to classical individual super-replication. The positive difference between the aggregation (sum) of individual superhedging prices and the Collective Super-replication price represents the value of cooperation.

Finally, we explain how these collective features can be associated with a broader class of risk measurement or cost assessment procedures beyond the superhedging framework. This leads to the notion of Collective Risk Measures, which generalize the idea of risk sharing and inf-convolution of risk measures.