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 HU Berlin, Institut für Mathematik, Hörsaal 1.115 (Rudower Chaussee 25) statt.
- Zeit: Donnerstag, 16 Uhr c.t. / 17 Uhr c.t.
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24.10.2024
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07.11.2024 16 Uhr c.t.
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David Hobson (University of Warwick) Portfolio optimization under transaction costs with recursive preferences
Abstract: The solution to the investment-consumption problem in a frictionless Black-Scholes market for an investor with additive CRRA preferences is to keep a constant fraction of wealth in the risky asset. But this requires continuous adjustment of the portfolio and as soon as transaction costs are added, any attempt to follow the frictionless strategy will lead to immediate bankruptcy. Instead as many authors have proposed the optimal solution is to keep the pair (cash, value of risky assets) in a no-transaction (NT) wedge.
We return to this problem to see what we can say about: When is the problem well-posed? Where does the NT wedge lie? How do the results change if we use recursive preferences? We introduce the shadow fraction of wealth and show how we can make significant progress towards the solution by focussing on this quantity. Indeed many of the qualitative features of the solution can described by looking at a quadratic whose parameters depend on the parameters of the problem.
This is joint work with Martin Herdegen and Alex Tse.
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07.11.2024 17 Uhr c.t. |
Johannes Muhle-Karbe (Imperial College London) Concave Cross Impact
Abstract: The price impact of large orders is well known to be a concave function of trade size. We discuss how to extend models consistent with this “square-root law” to multivariate settings with cross impact, where trading each asset also impacts the prices of the others. In this context, we derive consistency conditions that rule out price manipulation. These minimal conditions make risk-neutral trading problems tractable and also naturally lead to parsimonious specifications that can be calibrated to historical data. We illustrate this with a case study using proprietary CFM meta order data.
(Joint work in progress with Natascha Hey and Iacopo Mastromatteo)
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21.11.2024 16 Uhr c.t.
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Yonatan Shadmi (Imperial College London) Fluid limits of fragmented limit order markets
Abstract: Maglaras, Moallemi and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In this talk I will present the proof that, in the limit of small and frequent orders, the discrete system indeed converges to the fluid limit, which is characterized by a system of coupled nonlinear ODEs with singular coefficients at the origin. Moreover, I will discuss the temporal asymptotic stability for an arbitrary number of limit order books in that, over time, it converges to the stationary equilibrium state studied by Maglaras et al. |
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21.11.2024 17 Uhr c.t.
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Filippo de Feo (Luiss Guido Carli University, Milano) Optimal control of stochastic delay differential equations and applications to financial and economic models
Abstract: Optimal control problems involving Markovian stochastic differential equations have been extensively studied in the research literature; however, many real-world applications necessitate the consideration of path-dependent non-Markovian dynamics. In this talk, we consider an optimal control problem of (path-dependent) stochastic differential equations with delays in the state. To use the dynamic programming approach, we regain Markovianity by lifting the problem on a suitable Hilbert space. We characterize the value function $V$ of the problem as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, which is a fully non-linear second-order partial differential equation on a Hilbert space with an unbounded operator. Since no regularity results are available for viscosity solutions of these kinds of HJB equations, via a new finite-dimensional reduction procedure that allows us to use the regularity theory for finite-dimensional PDEs, we prove partial $C^{1,\alpha}$-regularity of $V$. When the diffusion is independent of the control, this regularity result allows us to define a candidate optimal feedback control. However, due to the lack of $C^2$-regularity of $V$, we cannot prove a verification theorem using standard techniques based on Ito’s formula. Thus, using a technical double approximation procedure, we construct functions approximating $V$, which are supersolutions of perturbed HJB equations and regular enough to satisfy a non-smooth Ito’s formula. This allows us to prove a verification theorem and construct optimal feedback controls. We provide applications to optimal advertising and portfolio optimization. We discuss how these results extend to the case of delays in the control variable (also) and discuss connections with new results of $C^{1,1}$-regularity of the value function and optimal synthesis for optimal control problems of stochastic differential equations on Hilbert spaces via viscosity solutions.
The talk is based on the following manuscripts:
F. de Feo, S. Federico, A. Święch, "Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models", SIAM J. Control Optim. 62 (2024), no. 3, 1490–1520.
F. de Feo, A. Święch, "Optimal control of stochastic delay differential equations: Optimal feedback controls", arXiv preprint arXiv:2309.05029 (2023).
F. de Feo, "Stochastic optimal control problems with delays in the state and in the control via viscosity solutions and applications to optimal advertising and optimal investment problems", Decis. Econ. Finance (2024) 31 pp.
F. de Feo, A. Święch, L. Wessels, "Stochastic optimal control in Hilbert spaces: $C^{1,1}$-regularity of the value function and optimal synthesis via viscosity solutions", arXiv preprint, arXiv:2310.03181 (2023).
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05.12.2024 16 Uhr c.t.
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Stefanos Theodorakopoulous (TU Berlin) Topics on mean-field and McKean–Vlasov BSDEs, and the backward propagation of chaos
Abstract: We shall present different versions of McKean-Vlasov and mean-field BSDEs of increasing generality, and the notion of backward propagation of chaos. We will then discuss some of the technical difficulties associated with the corresponding limit theorems and see some of their immediate corollaries |
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05.12.2024 17 Uhr c.t.
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Patrick Cheridito (ETH Zürich) Sentiment-based asset pricing
Abstract: We propose a continuous-time equilibrium model with a representative agent that is subject to stochastically fluctuating sentiments. Sentiments dynamically respond to past price movements and exhibit jumps, which occur more frequently when sentiments are disconnected from underlying fundamentals. We model feedback effects between asset prices and sentiment in both directions. Our analysis shows that in equilibrium, sentiments affect prices even though they have no direct impact on the asset’s fundamentals. Empirically, the equilibrium risk premia and risk-free rate respond to measurable shifts in sentiment in the direction predicted by the model.
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19.12.2024
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16.01.2025
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N.N.
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30.01.2025 16 Uhr c.t. |
Alexandros Saplaouras (ETH Zürich) The Itô Integral for Nonlinear Lévy Processes: Insights into the G-Lévy Framework
Abstract: Nonlinear Lévy processes, as established within the general framework by A. Neufeld and M. Nutz, offer a versatile foundation without restrictions on the characteristic triplets. Building on this foundational work, we focus specifically on G-Lévy processes, a concept introduced by S. Peng. Adopting Peng's approach, we construct the Itô integral with respect to G-Lévy processes and examine its associated properties. Alongside, we delve into results concerning the uniqueness of fully nonlinear integro-partial differential equations and briefly discuss the technical challenges.
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30.01.2025 17 Uhr c.t. |
Stefan Weber (Leibniz Universität Hannover) Robust Portfolio Selection Under Recovery Average Value at Risk
Abstract: We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical Average Value at Risk shows that portfolio selection under its recovery version allows financial institutions to better control the recovery of liabilities while still allowing for tractable computations. The talk is based on joint work with Cosimo Munari, Justin Plückebaum and Lutz Wilhelmy.
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13.02.2025
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N.N. |
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Interessenten sind herzlich eingeladen.
Für Rückfragen wenden Sie sich bitte an:
Frau Sabine Bergmann
bergmann@math.hu-berlin.de
Telefon: 2093 45450
Telefax: 2093 45451