FS Stochastische Analysis und Stochastik der Finanzmärkte
Bereich für Stochastik
P. BANK, Ch. BAYER, D. BECHERER, P. FRIZ, P. HAGER, U. HORST, D. KREHER
 Das Seminar findet an der TU Berlin, Institut für Mathematik, Raum MA 042 (Straße des 17. Juni 136) statt.
 Zeit: Donnerstag, 16 Uhr c.t. / 17 Uhr c.t.
18.04.2024 16. Uhr c.t. 
Alexandre Pannier (Université Paris Cité) A pathdependent PDE solver based on signature kernels
Abstract: We develop a provably convergent kernelbased solver for pathdependent PDEs (PPDEs). Our numerical scheme leverages signature kernels, a recently introduced class of kernels on pathspace. Specifically, we solve an optimal recovery problem by approximating the solution of a PPDE with an element of minimal norm in the signature reproducing kernel Hilbert space (RKHS) constrained to satisfy the PPDE at a finite collection of collocation paths. In the linear case, we show that the optimisation has a unique closedform solution expressed in terms of signature kernel evaluations at the collocation paths. We prove consistency of the proposed scheme, guaranteeing convergence to the PPDE solution as the number of collocation points increases. Finally, several numerical examples are presented, in particular in the context of option pricing under rough volatility. Our numerical scheme constitutes a valid alternative to the ubiquitous Monte Carlo methods. Joint work with Cristopher Salvi (Imperial College London). 

18.04.2024 17 Uhr c.t.

Nils Detering (Universität Düsseldorf) Local Volatility Models for Commodity Forwards
Abstract: We present a dynamic model for forward curves in commodity markets, which is defined as the solution to a stochastic partial differential equation (SPDE) with statedependent coefficients, taking values in a Hilbert space H of real valued functions. The model can be seen as an infinite dimensional counterpart of the classical local volatility model frequently used in equity markets. We first investigate a class of pointwise operators on H, which we then use to define the coefficients of the SPDE. Next, we derive growth and Lipchitz conditions for coefficients resulting from this class of operators to establish existence and uniqueness of solutions. We also derive conditions that ensure positivity of the entire forward curve. Finally, we study the existence of an equivalent measure under which related traded, 1dimensional projections of the forward curve are martingales. 

02.05.2024 17 Uhr c.t. 
Katharina Oberpriller (Universität München) Reducedform framework and affine processes with jumps under model uncertainty
Abstract: We introduce a sublinear conditional operator with respect to a family of possibly nondominated probability measures in presence of multiple ordered default times. In this way we generalize the results in [3] where a consistent reducedform framework under model uncertainty for a single default is developed. Moreover, we present a probabilistic construction of Rdvalued nonlinear affine processes with jumps, which allows to model intensities in a reducedform framework. This yields a tractable model for Knightian uncertainty for which
the sublinear expectation of a Markovian functional can be calculated via a partial integrodifferential equation. This talk is based on [1] and [2]. 

02.05.2024

N.N. 

16.05.2024 16 Uhr c.t.

Sina Dahms, Matthias Drees, and Lea Fernandez (B & W Deloitte GmbH, Berlin)
Extrem value theory in the insurance sector
Abstract: Dusty insurance industry or buzzword bingo? Not with us! We work both in the world of insurance industry and management consulting, which means for us no two days are the same. Our practice supports many of the world’s leading organizations by using modern data analytics and complex mathematical models. Thereby we quantify the risks of the insurance industry, making risks visible and 

16.05.2024

N.N. 

30.05.2024 16 Uhr c.t.

Marko Weber (National University of Singapore) General Equilibrium with Unhedgeable Fundamentals and Heterogeneous Agents
Abstract: We examine the implications of unhedgeable fundamental risk, combined with agents' heterogeneous preferences and wealth allocations, on dynamic asset pricing and portfolio choice. We solve in closed form a continuoustime general equilibrium model in which unhedgeable fundamental risk affects aggregate consumption dynamics, rendering the market incomplete. Several longlived agents with heterogeneous riskaversion and timepreference make consumption and investment decisions, trading risky assets and borrowing from and lending to each other. We find that a representative agent does not exist. Agents trade assets dynamically. Their consumption rates depend on the history of unhedgeable shocks. Consumption volatility is higher for agents with preferences and wealth allocations deviating more from the average. Unhedgeable risk reduces the equilibrium interest rate only through agents' heterogeneity and proportionally to the crosssectional variance of agents' preferences and allocations. 

30.05.2024 17 Uhr c.t. 
Shige Peng (Shandong University) Solving probability measure uncertainty by nonlinear expectations
Abstract: In 1921, economist Frank Knight published his famous "Uncertainty，Risk and Profit" in which his challenging is still largely open.In this talk we explain why nonlinear expectation theory provides a powerful and fundamentally important mathematical tool to this century problem.


13.06.2024 16 Uhr c.t. 
Eduardo Abi Jaber (École Polytechnique, Palaiseau) Stochastic Fredholm equations: a passepartout for propagator models with crossimpact, constraints and meanfield interactions
Abstract: We will provide explicit solutions to certain systems linear stochastic Fredholm equations. We will then show the versatility of these equations for solving various optimal trading problems with transient impact including: (i) crossimpact (multiple assets), (ii) constraints on the inventory and trading speeds, and (iii) Nplayer game and meanfield interactions (multiple traders).
Based on joint works with Nathan De Carvalho, Eyal Neuman, Huyên Pham, Sturmius Tuschmann, and Moritz Voss.


13.06.2024 17 Uhr c.t.

Likai Jiao (HU Berlin) An infinitedimensional price impact model
Abstract: In this talk, we introduce an infinitedimensional price impact process as a kind of Markovian lift of nonMarkovian 1dimensional price impact processes with completely monotone decay kernels. In an additive price impact scenario, the related optimal control problem is extended and transformed into a linearquadratic framework. The optimal strategy is characterized by an operatorvalued Riccati equation and a linear backward stochastic evolution equation (BSEE). By incorporating stochastic inflow, the BSEE is simplified into an infinitedimensional ODE. With appropriate penalizations, the wellposedness of the Riccati equation is wellknown. This is a joint work with Prof. Dirk Becherer and Prof. Christoph Reisinger. 

27.06.2024 16 Uhr c.t. 
Libo Li (UNSW Sydney) Vulnerable European and American Options in a Market Model with Optional Hazard
Abstract: We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying market model is incomplete and frictionless, we obtain duality results linking the upper price of a vulnerable European option with the price of an American option whose exercise times are constrained to times at which the external termination can happen with a nonzero probability. Similarly, the upper and lower prices for a vulnerable American option are linked to the price of an American option and a game option, respectively. In particular, the minimizer of the game option is only allowed to stop at times which the external termination may occur with a nonzero probability. 

27.06.2024 17 Uhr c.t. 
Benjamin Jourdan (University of ParisEst) Convexity propagation and convex ordering of onedimensional stochastic differential equations
Abstract: We consider driftless onedimensional stochastic differential equations. We first recall how they propagate convexity at the level of single marginals. We show that some spatial convexity of the diffusion coefficient is needed to obtain more general convexity propagation and obtain functional convexity propagation under a slight reinforcement of this necessary condition. Such conditions are not needed for directional convexity..


11.07.2024 16 Uhr c.t.

Tiziano de Angelis (University of Turin) Linearquadratic stochastic control with state constraints on finitetime horizon
Abstract: We obtain a probabilistic solution to linearquadratic optimal control problems with state


11.07.2024 17 Uhr c.t.

Jianniao Qui (University of Calgary) Consensusbased optimization for equilibrium points of games
Abstract: In this talk, we will introduce ConsensusBased Optimization (CBO) for minmax problems, 




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Frau Sabine Bergmann
bergmann@math.huberlin.de
Telefon: 2093 45450
Telefax: 2093 45451