Stefan
Weber
Leibniz Universität Hannover
Forschungsseminar Stochastische Analysis und Stochastik der Finanzmärkte 📅
Institute
Head
P. Bank,
Ch. Bayer,
D. Becherer,
P. Friz,
P. Hager,
U. Horst, and
D. Kreher
Usual time
Thursdays at 16:15 and 17:15
Usual venue
TU Berlin, Institut für Mathematik, Raum MA 042 (Straße des 17. Juni 136)
Number of talks
17
January 2025
December 2024
Patrick
Cheridito
ETH Zürich
November 2024
Yonatan
Shadmi
Imperial College London
Johannes
Muhle-Karbe
Imperial College London
David
Hobson
University of Warwick
July 2024
Jianniao
Qui
University of Calgary
Consensus-based optimization for equilibrium points of games
Abstract.
In this talk, we will introduce Consensus-Based Optimization (CBO) for min-max problems, a novel multi-particle, derivative-free optimization method that can provably identify global equilibrium points. This paradigm facilitates the transition to the mean-field limit, making the method amenable to theoretical analysis and providing rigorous convergence guarantees under reasonable assumptions about the initialization and the objective function, including nonconvex-nonconcave objectives. Additionally, numerical evidence will be presented to demonstrate the algorithm’s effectiveness. This talk is based on joint works with Giacomo Borghi, Enis Chenchene, Hui Huang, and Konstantin Riedl.
Tiziano
de Angelis
University of Turin
Linear-quadratic stochastic control with state constraints on finite-time horizon
Abstract.
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set D ⊆ [0, T] × Rd, a diffusion X in Rd must be linearly controlled in order to keep the time-space process (t, Xt) inside the set C := ([0, T] × Rd) \ D, while at the same time minimising an expected cost that depends on the state (t, Xt) and it is quadratic in the speed of the control exerted. We find an explicit probabilistic representation for the value function and the optimal control under a set of mild sufficient conditions concerning the coefficients of the underlying dynamics and the regularity of the set C. Fully explicit formulae are presented in some relevant examples. (Joint work with Erik Ekström, University of Uppsala, Sweden)
June 2024
Benjamin
Jourdan
University of Paris-Est
Convexity propagation and convex ordering of one-dimensional stochastic differential equations
Abstract.
We consider driftless one-dimensional 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. This is a joint work with Gilles Pagès.
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 non-zero 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 non-zero probability.
Likai
Jiao
HU Berlin
An infinite-dimensional price impact model
Abstract.
In this talk, we introduce an infinite-dimensional price impact process as a kind of Markovian lift of non-Markovian 1-dimensional 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 linear-quadratic framework. The optimal strategy is characterized by an operator-valued Riccati equation and a linear backward stochastic evolution equation (BSEE). By incorporating stochastic in-flow, the BSEE is simplified into an infinite-dimensional ODE. With appropriate penalizations, the well-posedness of the Riccati equation is well-known. This is a joint work with Prof. Dirk Becherer and Prof. Christoph Reisinger.
Eduardo
Abi Jaber
École Polytechnique, Palaiseau
Stochastic Fredholm equations: a passe-partout for propagator models with cross-impact, constraints and mean-field 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) cross-impact (multiple assets), (ii) constraints on the inventory and trading speeds, and (iii) N-player game and mean-field interactions (multiple traders). Based on joint works with Nathan De Carvalho, Eyal Neuman, Huyên Pham, Sturmius Tuschmann, and Moritz Voss.
May 2024
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.
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 continuous-time general equilibrium model in which unhedgeable fundamental risk affects aggregate consumption dynamics, rendering the market incomplete. Several long-lived agents with heterogeneous risk-aversion and time-preference 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 cross-sectional variance of agents' preferences and allocations.
Sina
Dahms
B & W Deloitte GmbH, Berlin
and
Matthias
Drees
B & W Deloitte GmbH, Berlin
and
Lea
Fernandez
B & W Deloitte GmbH, Berlin
Extreme 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 manageable. We work together with our clients to assess their strategic priorities, increase economic value, optimize capital, and drive organizational performance. Sina Dahms, Matthias Drees, and Lea Fernandez from Deloitte will talk about extreme value theory and its applications in insurance and will give exclusive insights into the day-to-day work of an actuarial consultant. Sina has a PhD in financial mathematics from HU Berlin, Matthias holds degrees in mathematics and physics from universities in Munich, Cambridge and Tokyo, and Lea recently finished her studies of mathematics and physics at the TU Berlin.
Katharina
Oberpriller
Universität München
Reduced-form framework and affine processes with jumps under model uncertainty
Abstract.
We introduce a sublinear conditional operator with respect to a family of possibly non-dominated probability measures in presence of multiple ordered default times. In this way we generalize the results in [3] where a consistent reduced-form framework under model uncertainty for a single default is developed. Moreover, we present a probabilistic construction of Rd-valued non-linear affine processes with jumps, which allows to model intensities in a reduced-form framework. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation. This talk is based on [1] and [2].
April 2024
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 state-dependent 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 point-wise 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, 1-dimensional projections of the forward curve are martingales. Our approach encompasses a wide range of specifications, including a Hilbert-space valued counterpart of a constant elasticity of variance (CEV) model, an exponential model, and a spline specification which can resemble the S shaped local volatility function that well reproduces the volatility smile in equity markets. A particularly pleasant property of our model class is that the one-dimensional projections of the curve can be expressed as one-dimensional stochastic differential equation. This provides a link to models for forwards with a fixed delivery time for which formulas and numerical techniques exist. In a first numerical case study we observe that a spline based, S shaped local volatility function can calibrate the volatility surface in electricity markets. Joint work with Silvia Lavagnini (BI Norwegian Business School)
Alexandre
Pannier
Université Paris Cité
A path-dependent PDE solver based on signature kernels