,,Varianzapproximationen des ML-Schätzers im Admixture-Modell"
Donnerstag, 5.3.26, 10:00-11:30, Seminarraum 232
Master-Vortrag "Convergence rate analysis of the nonparametric maximum likelihood estimator with external data"
Dienstag, 27.1.26, 15:15-16:45, Seminarraum 232
Master-Vortrag "Sharp nonparametric testing for constant volatility"
Dienstag, 27.1.26, 14:15-15:45, Seminarraum 232
Bayesian estimation with set-valued observations
Mittwoch, 3.12.25, 16:00-17:30, Seminarraum 226 (HH10)
In this work, we develop a Bayesian estimation framework in which the observable quantity is a random set rather than a classical random vector. The motivation comes from expert-opinion modelling in highly uncertain environments—such as robotic risk management—where experts typically provide confidence intervals or other set-valued assessments for key risk factors. We first show that, under suitable assumptions, the standard Bayesian update formula remains valid and does not require substantial modification compared to the classical setting where both signal and observation take values in Polish spaces. However, whereas these assumptions (such as absolute continuity of the conditional distribution of the observation given the signal) are straightforward to verify for vector-valued observations, the set-valued case requires a more delicate, case-by-case analysis.
We then establish that the required regularity conditions indeed hold for a broad class of random sets, including random intervals, balls, finite sets, and more generally convex compact sets. Particular attention is devoted to finite-valued random sets, which are more challenging and also appear in Bayesian filtering within the FISST framework introduced by Ronald P. S. Mahler in the mid-1990s.
Work together with Prof. Dr. Cagin Ararat
Asset-liability management with Epstein-Zin utility under stochastic interest rate and unknown market price of risk
Mittwoch, 26.11.25, 16:00-17:30, Seminarraum 226 (HH10)
In this talk we present a stochastic control problem with Epstein-Zin recursive utility under partial information (unknown market price of risk), in which an investor is constrained to a liability at the end of the investment period. Introducing liabilities is the main novelty of the model and appears for the first time in the literature of recursive utilities. Such constraint leads to a coupled forward-backward stochastic differential equation (FBSDE), which well-posedness has not been addressed in the literature. We derive an explicit solution to the FBSDE, contrasting with the existence and uniqueness results with no explicit expression of the solutions typically found in most related literature. Moreover, under minimal additional assumptions, we obtain the Malliavin differentiability of the solution of the FBSDE. We solve the problem completely and find the expression of the controls and the value function. Finally, we determine the utility loss that investors suffer from ignoring the fact that they can learn about the market price of risk.