Filter off: No filter for categories

Periodic partitions with minimal perimeterMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

I will discuss existence and regularity of fundamental domains which minimize a general perimeter functional in a homogeneous metric measure space. In the planar case I will give a detailed description of the domains which are minimal for a general anisotropic perimeter.

An Eulerian Method for Mean Field GamesMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

The Recovery Potential for Underfunded Pension PlansOnline: attend (Meeting-ID: 644 3815 8134 Password: 318315)2.02.03 (Parkring 11, 85748 Garching)

We investigate whether risk-taking for resurrection type of risk preference (non-constant risk aversion) can increase the probability of achieving inflation-indexed pension benefits at retirement, especially when the starting position is underfunded. By maximizing the expected utility of the ratio of final wealth to a close approximation of this inflation-indexed target fund, we find that this non-constant risk aversion type of utility gives a high degree of certainty about achieving a certain percentage of this desired target fund. The CRRA utility is too risk-averse to overcome under-funding.

Near-Optimal Asset Allocation in Financial Markets with Trading Constraints Online: attend (Meeting-ID: 644 3815 8134 Password: 318315)2.02.03 (Parkring 11, 85748 Garching)

We develop a dual-control method for approximating investment strategies in multidimensional financial markets with convex trading constraints. The method relies on a projection of the optimal solution to an (unconstrained) auxiliary problem to obtain a feasible and near-optimal solution to the original problem. We obtain lower and upper bounds on the optimal value function using convex duality methods. The gap between the bounds indicates the precision of the near-optimal solution. We illustrate the effectiveness of our method in a market with different trading constraints such as borrowing, short-sale constraints and non-traded assets. We also show that our method works well for state-dependent utility functions.

Diffusionen auf Mannigfaltigkeiten für die Steinsche Methode der austauschbaren PaareB 252 (Theresienstr. 39, 80333 München)

Ziel des Vortrags ist es, mithilfe von Diffusionen auf Riemann Mannig- faltigkeiten eine Familie von austauschbaren Paaren im R^d für die Steinsche Meth- ode der austauschbaren Paare zu konstruieren und daraus eine Abschätzung zu gewinnen. Um die nötigen Schritte zu erklären, werden in dem Vortrag zuerst die Steinsche Methode vorgestellt und einige Grundlagen zu Mannigfaltigkeiten in Zusam- menhang mit Stochastik erklärt. Im Anschluss daran definiere ich eine geeignete Diffusion, erkläre ihre Eigenschaften, bilde sie auf R^d ab und wende die Steinsche Meth- ode der austauschbaren Paare an. Das Vorgehen entstammt dem Artikel ”Constructing exchangeable pairs by diffusion on manifold and its application” von Weitao Du, 2006.

Optimal consumption, investment, and insurance under state-dependent risk aversionOnline: attend (Meeting-ID: 644 3815 8134 Password: 318315)2.02.03 (Parkring 11, 85748 Garching)

We formalize a consumption-investment-insurance problem with the distinction of a state-dependent relative risk aversion. The state-dependence refers to the state of the finite state Markov chain that also formalizes insurable risks such as health and lifetime uncertainty. We derive and analyze the implicit solution to the problem, compare it with special cases in the literature, and illustrate the range of results in a disability model where the relative risk aversion is preserved, decreases, or increases upon disability. We also discuss whether the approach is appropriate to deal with uncertainty in relative risk aversion and consider some alternative ideas.

Optimal Consumption, Investment, Housing and Life Insurance Purchase Decisions for a Couple with Dependent MortalityOnline: attend (Meeting-ID: 644 3815 8134 Password: 318315)2.02.03 (Parkring 11, 85748 Garching)

In this paper we study an optimisation problem for a couple including two breadwinners with uncertain lifetimes. Both breadwinners need to choose the optimal strategies for consumption, investment, housing and life insurance purchasing during to maximise the utility. In this paper, the prices of housing assets and investment risky assets are assumed to be correlated. These two breadwinners are considered to have dependent mortality rates to include the breaking heat effect. The method of copula functions is used to construct the joint survival functions of two breadwinners. The analytical solutions of optimal strategies can be achieved, and numerical results are demonstrated.

Matchings of Students and Seminars: a Linear Programming ApproachMI 02.04.011 (Boltzmannstr. 3, 85748 Garching)

The goal of this project was, assuming both a group of seminars and a group of students give preferences over the agents in the other group they are interested in, to find an homogeneous assignment of participants and seminars which addresses the situation of each seminar and each student as best as possible. This problem is a generalization of the classical Hospitals/Residents Problem, where we allowed indifference in the preference relations of each agent, assigned an arbitrary but fixed number of types to each student (each belonging to a category, e.g. study program, exchange student or not, etc) and were interested in allowing each seminar to state the minimal number of participants they would require to be held. The impact of all these changes was studied and the resulting problem formulated as a Linear Program.

Diffeomorphism groups of discsA027 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

The closed n-dimensional disc is the simplest smooth compact n-manifold and yet, despite continuous efforts of geometers and topologists since the beginning of the 60s, its group of symmetries (the topological group of diffeomorphisms) is still little understood. Over time it has become apparent that, although rooted in geometry and topology, the study of these groups is closely linked to several other areas of mathematics. In this talk, after giving a general introduction to the subject aimed at a broad audience, I will outline some of these connections and survey recent advances in the study of diffeomorphism groups of discs in relation to algebraic K-theory, exotic Pontryagin classes, and graph complexes à la Kontsevich.

Market-consistent pricing with acceptable riskB349 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given securities market. Trading is subject to nonproportional transaction costs and portfolio constraints and full replication by way of market instruments is not always possible. Rationality is defined in terms of consistency with market prices and acceptable risk thresholds. We obtain a direct and a dual description of market-consistent prices with acceptable risk. The dual characterization requires an appropriate extension of the classical Fundamental Theorem of Asset Pricing where the role of arbitrage opportunities is played by good deals, i.e., costless investment opportunities with acceptable risk-reward tradeoff. In particular, we highlight the importance of scalable good deals, i.e., investment opportunities that are good deals regardless of their volume. The talk is based on joint work with Maria Arduca (LUISS Rome). *For participation on Zoom, please contact Felix Liebrich (liebrich@math.lmu.de)

TBA2.02.01 (Parkring 11, 85748 Garching-Hochbrück)

TBA

Metastability for Loss Networks2.02.01 (Parkring 11, 85748 Garching-Hochbrück)

We consider a fully-connected loss network with dynamic alternative routing, each link of capacity K. Calls arrive to each link {i, j} at rate λ independently and depart at rate 1. If the link is full upon arrival, a third node k is chosen uniform and the call is routed via k: it uses a unit of capacity on both {i, k} and {k, j} if both have spare capacity; otherwise, the call is lost. This is a model for telephone networks, implemented by BT in the 1990s. We analyse the asymptotics of the mixing time of this process, depending on the traffic intensity α := λ/K. In particular, we determine a phase transition at an explicit threshold α*: there is fast mixing if α < α* or α > 1, but metastability if α* < α < 1. We also discuss a fixed for metastability—ie, an adjustment to the model which removes the slow-mixing phase. Again, this was implemented by BT in the UK telephone network.

An action functional for nonlinear dislocation dynamicsMI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

Dislocations are the physical defects whose motion and interaction are responsible for the plasticity of crystalline solids. The physics can be characterized by a system of nonlinear PDE which does not naturally emanate from a variational principle. We describe the development of a family of dual variational principles for this primal system with the property that the Euler-Lagrange system of each of its members is the primal system in a well-defined sense. We illustrate the main idea of the scheme and its viability by applying it to compute approximate solutions to the linear heat, and first-order, scalar wave equations, and 1-d, nonconvex elastostatics.

Causal Inference: Challenges and OpportunitiesBC1 2.01.10 (Parkring 11, 85748 Garching)

Causal inference is a branch of machine learning and statistics that aims to develop theoretical models and practical algorithms to infer the statistical causal dynamics in complex systems. The incorporation of causality in learning is what predominantly sets human judgment apart from machines. In this talk, I will briefly explain new developments in causal discovery, the problem of identifiability and inverse aka experimental design, causal transfer learning, and Granger’s notion of causality in time series and discuss how his formulation can go beyond linear dynamics. As an application, I will present an application of causality in imitation learning and developing self-driving vehicles.

t.b.a.BC1 2.01.10 (Parkring 11, 85748 Garching)

t.b.a.

Bayesian nonparametric models derived from completely random measuresOnline: attend (Meeting-ID: 644 3815 8134 Password: 318315)2.02.03 (Parkring 11, 85748 Garching)

The Dirichlet process represents the cornerstone of Bayesian Nonparametrics and is used as main ingredient in a wide variety of models. The many generalizations of the Dirichlet proposed in the literature aim at overcoming some of its limitations and at increasing the models' flexibility. In this talk we provide an overview of a large set of such generalizations by using completely random measures as a unifying concept. All the considered models can be seen as suitable transformations of completely random measures and this allows to highlight interesting distributional structures they share a posteriori in several statistical problems ranging from density estimation and clustering to survival analysis and species sampling. Furthermore, we discuss some natural approaches, which rely on additive, hierarchical and nested structures, to derive dependent versions of Bayesian nonparametric models derived from completely random measures.