• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

Angiogenesis is the process by which the body generates new blood vessels. This occurs in the context of wound healing where, of course, it is beneficial to the body. However, it can also occur in cancer where it can enhance delivery of nutrients to the cancer and enable cancer cells to infiltrate the blood system and metastasize to vital organs, leading to the often fatal secondary tumours. Understanding this process is a challenge for both experimentalists and theoreticians. I will review some recent work we have done on this problem which includes generating a new partial differential equation model for the so-called ``snail-trail'' movement of blood vessel cells to the tumour (Pillay et al, 2017), by developing a continuuum model of the process from a discrete description. I will then present a computational multiscale model for a key experimental assay that is used by experimentalists to measure the efficacy of anti-angiogenesis drugs and use it to make predictions (Grogan et al, 2018; 2017).

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

TBA

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

Oncogenes perturb molecular mechanisms to drive neoplastic initiation and progression. Chromosomal rearrangements are frequent events in cancer, and can result in the expression of fusion proteins. Fusion proteins represent neomorphic protein variants with aberrant activities and are often drivers of oncogenesis. Acute myeloid leukemia (AML) is an aggressive cancer of the white blood cell lineage that is associated with poor prognosis. While AML features a particular high prevalence of fusion proteins, it is largely unknown how the majority of AML fusion proteins rewire the molecular machinery of normal blood cells to induce leukemia. We hypothesize that oncogenic mechanisms of AML fusion proteins are hard-wired in specific networks of physical, genetic and epigenetic interactions with key effector proteins. Functional exploration of these networks by systematic comparative approaches will provide new insights into cellular processes that depend on critical effector proteins among these networks. The goal of our research is a comprehensive systems-level investigation of oncogenic mechanisms employed by AML fusion proteins. We have established a robust experimental pipeline for the rapid characterization of fusion oncoproteins in a multilayered, global fashion. We use modern genetic tools to generate advanced cell and animal models for tunable expression of AML fusion proteins. Fusion protein-dependent changes in cellular topologies are charted by proteomic and transcriptomic approaches. In parallel, genome-scale loss-of function CRISPR/Cas9 screening is used to identify critical effectors of leukemogenesis. High-confidence candidates are validated using a wide array of different approaches, including studies in primary patient-derived leukemia cells. Results from this pipeline provide evidence for its robust validity, but also for its translational impact, strongly implying that this approach will contribute to an improved understanding of oncogenesis.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

In the majority of cancers, secondary tumors (metastases) and associated complications are the main cause of death. To design the best therapy for a given patient, one of the major current challenge is to estimate, at diagnosis, the eventual burden of invisible metastases and the future time of emergence of these, as well as their growth speed. In this talk, I will present the current state of research efforts towards the establishment of a predictive computational tool for this aim. I will first shortly present the model used, which is based on a physiologically-structured partial differential equation for the time dynamics of the population of metastases, combined to a nonlinear mixed-effects model for statistical representation of the parameters’ distribution in the population. Then, I will show results about the descriptive power of the model on data from clinically relevant ortho-surgical animal models of metastasis (breast and kidney tumors). The main part of my talk will further be devoted to the translation of this modeling approach toward the clinical reality. Using clinical imaging data of brain metastasis from non-small cell lung cancer, several biological processes will be investigated to establish a minimal and biologically realistic model able to describe the data. Integration of this model into a biostatistical approach for individualized prediction of the model’s parameters from data only available at diagnosis will also be discussed. Together, these results represent a step forward towards the integration of mathematical modeling as a predictive tool for personalized medicine in oncology.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

In this talk, we investigate the link between multi-scale models for tumor growth. We start from a microscopic model where cells are modelled as 2D spheres undergoing short range repulsion and cell division. We derive the associated macroscopic dynamics leading to a porous media type equation. As the macroscopic equation obtained through usual derivation method fails at providing the correct qualitative behavior, we propose a modified version of the macroscopic equation introducing a density threshold for the repulsion. We numerically validate the new formulation by comparing the solutions of the micro- and macro- dynamics. Moreover, we study the asymptotic behavior of the dynamics as the repulsion between cells becomes singular (leading to non-overlapping constraints in the microscopic model). We show formally that such asymptotic limit leads to a Hele-Shaw type problem for the macroscopic dynamics. The numerical simulations reveal an excellent agreement between the micro- and macro- descriptions, validating the formal derivation of the macroscopic model. The macroscopic model derived here therefore enables to overcome the problem of large computational time raised by the microscopic model, but stays closely linked to the microscopic dynamics.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

Cancer imaging has undergone major paradigm shifts within the last decade. Hybrid imaging techniques, and in particular, PET/CT (positron emission tomography / computed tomography) with the glucose analogue radiotracer [18F]FDG is now an integral part of the management guidelines for patients with different cancers, with a particular emphasis on the early detection of treatment effects on the tumor. Novel PET radiotracers that are specific for certain types of cancer – such as [68Ga]PSMA for prostate cancer – are currently being evaluated in clinical trials. Notably, though visual image interpretation is still the clinical standard, there is now a trend towards the use of quantitative data extracted from diagnostic images. The recently introduced PET/MRI (magnetic resonance imaging) is of particular interest in that regard, because it offers information on tissue properties such as cell density and blood flow in addition to the metabolic information provided by PET. The combination of quantitative parameters extracted from MRI and PET may not only improve non-invasive, image-based characterization of tumor heterogeneity, but may also improve evaluation of the effects of novel types of treatment. This multi-parametric approach also provides an ideal basis for radiomics – i.e., computer-assisted image analysis, and based on it, recognition of mathematical image patterns that are related to tumor characteristics. This novel approach to image interpretation, which is aided by advanced techniques such as artificial neural networks, has the potential to contribute significantly to the success of precision medicine, and the welfare of patients.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

In this talk we present our work on the dynamics of tumor and immune cell interactions [1-4]. A hybrid probabilistic cellular automaton model describing the spatio-temporal evolution of tumor growth and its interaction with the cell-mediated immune response is developed. The model parameters are adjusted to an ordinary differential equation model, which has been previously validated [1] with in vivo experiments and chromium release assays. The cellular automaton is used to perform in silico experiments which, together with mathematical analyses, allow us to characterize the rate at which a tumor is lysed by a population of cytotoxic immune cells [2-3]. Finally, the transient and asymptotic dynamics of the cell-mediated immune response to tumor growth is considered [4]. The cellular automaton model is used to investigate and discuss the capacity of the cytotoxic cells to sustain long periods of tumor mass dormancy, as commonly observed in recurrent metastatic disease. This is a joint work with Alvaro G. López and Miguel A. F. Sanjuán.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

Glioblastoma may have wide-spread effects on the cortical organization and cognitive function since even focal lesions impact the brains’ functional network architecture. Currently, our understanding of the interaction between tumor lesions and their impact on the functional connectome is limited. Hence, we used 3 Tesla resting-state functional magnetic resonance imaging to evaluate the functional connectivity structure of 15 patients with glioblastoma. We further tracked the functional characteristics of six patients over time using bimonthly follow-up examinations. We found changes in resting-state networks to be highly symmetric and mirrored by changes in the cerebellum. Patients shared a pattern of network deterioration after surgery, with subsequent recovery at the first follow-up examination. Additionally, we showed that glioblastoma has a global effect on the functional connectivity structure of the individual patient, which might serve as sensitive early marker of tumor recurrence. Of note, local tumor recurrence coincided with network deterioration before structural changes were apparent upon imaging. In summary, our results demonstrate how the functional connectome is affected by focal lesions, and that it might be exploited as an early predictor of local tumor recurrence. This renders the individual patient’s functional connectome a promising novel biomarker for the longitudinal patient follow-up in order to support early informed treatment decisions.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

To tackle the question of drug resistance in cancer, I will present an adaptive dynamic framework to represent the evolution in phenotype of cell populations, that allows to follow the instantaneous distribution and asymptotic behaviour of drug resistance phenotype(s) in the cell population. Such phenotypes evolve under drug pressure towards either established or transient, possibly reversible, drug tolerance, a behaviour taken into account by the models we design to allow for therapeutic control. Optimal control strategies describing the combination of different categories of drugs on specified cell functional targets (thus far cytotoxics, that act on death terms, and cytostatics, that act on proliferation terms) are proposed, aiming at minimising a tumour cell population while limiting both unwanted toxic side effects on healthy cell populations and occurrence of drug resistance in cancer cell populations. The models used for these representations, their asymptotic properties and their theoretical therapeutic control are integro-differential (non-local Lotka-Volterra-like) or PDE models (reaction-diffusion models with or without advection). Finally, I will present some transdisciplinary challenges of cancer modelling that should concern mathematicians, cell biologists, evolutionary biologists and oncologists, aiming to go beyond the present state of the art in the treatments of cancer.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

Anemia associated with chronic diseases is the second most prevalent anemia in the world after anemia caused by iron deficiency. Advanced stages of diseases such as chronic kidney disease (CKD) and cancer coincide with a high prevalence of severe anemia that results in fatigue, reduced quality of life and decreased treatment responses in patients. Two therapeutic options are available to manage anemia: blood transfusion and treatment with erythropoiesis stimulating agents (ESAs) in combination with iron supplementation. However, adverse events and increased risk of mortality have been reported for blood transfusions and ESAs. Decisions on the clinical treatment should be based on the specific benefit-to-risk ratio of each patient, which is complicated to assess due to the heterogeneity of the patients, the lack of prognostic markers and the dynamics of comorbidities associated with the diseases. We developed a multiscale mathematical model that links mechanistic insights at the cellular scale to response at the body level to guide clinical decisions based on the prediction of the response to the available therapeutic options. The mathematical model stratifies patients based on the estimation of two patient specific dynamic parameters. These parameters are estimated by the mathematical model based on the time-course of the haemoglobin (Hb) values, CRP, iron values and scheduled chemotherapy in each patient. These two patient specific parameters reflect the anaemic status of the patient as well as the capability to respond to treatment with ESAs. The model is capable to propose optimized personalized interventions for anaemia management in lung cancer and CKD patients.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

In cancer research most efforts are devoted on the decipher of the IntraTumoral Heterogeneity (ITH). In ITH the action of the evolutionary forces of mutation and selection are essential to determinant the tumor progression, diagnosis and treatment. ITH gives rise to cancer cell populations with distinct genotypic and metabolic characteristics contributing to the failure of cure, by initiating phenotypic diversity and enabling more aggressive and drug resistant clones. I will present multi-scale models of cancer linking the tumor growth to the intracellullar signalling and metabolic events to genomic profiles. The models consider several heterogenous omics data (metabolomics, proteomics, transcriptomics, genomics) to investigate the ITH associated with different genomic and metabolic traits.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

Mathematical models of biological systems are often validated by fitting the model to the average of an (often small) experimental dataset. Here we ask the question of whether predictions made from a model fit to the average of a dataset are actually applicable in samples that deviate from the average. We will explore this in the context of a murine model of melanoma treated with oncolytic viruses and dendritic cell injections. We have hierarchically developed a system of ordinary different equations to describe the average of this experimental data, and optimized treatment subject to clinical constraints. Using a virtual population method, we explore the robustness of treatment response to the predicted optimal protocol; that is, we quantify the extent to which the optimal treatment protocol elicits the same qualitative response in virtual populations that deviate from the average. We find that our predicted optimal is not robust and in fact is potentially a dangerous protocol for a fraction of the virtual populations. However, if we consider a different drug dose than used in the experiments, we are able to identify an optimal protocol that elicits a robust anti-tumor response across virtual populations.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

As the spinal cord grows during embryonic development, an elaborate pattern of molecularly distinct neuronal precursor cells forms along the DV axis. This pattern depends both on the dynamics of a morphogen-regulated gene regulatory network, and on tissue growth. We study how these processes are coordinated. Our data revealed that during mouse and chick development the gene expression pattern changes but does not scale with the overall tissue size. These changes in the pattern are sequentially controlled by distinct mechanisms. Initially, neural progenitors integrate signaling from opposing morphogen gradients to determine their identity by using a mechanism equivalent to maximum likelihood decoding. This strategy allows accurate assignment of position along the patterning axis and can account for the observed precision and shifts of pattern. During the subsequent developmental phase, cell-type specific regulation of differentiation rate, but not proliferation, elaborates the pattern.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

TBA

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

In this talk, I focus on current biological problems and on how to use mathematical modeling to analyze a variety of pressing questions arising from oncology, developmental pattern formation and population ecology. I first discuss novel mathematical models for cancer growth dynamics and heterogeneity. These studies rely on evolutionary principles and shed light on 3D hepatic tumor dynamics, spatial heterogeneity and tumor invasion, and single cancer cell responses to antimitotic therapies. We also develop mathematical models that quantitatively demonstrate how the interplay between non-genetic instability, stress-induced adaptation, and selection leads to the transient and reversible phenotypic evolution of cancer cell populations exposed to therapy. Finally, we study control techniques for optimal therapeutic administration.

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

• Thematic program: Mathematical models in Biology and Medicine (2018/2019)
• Event: Workshop on "Mathematical Models in Cancer" (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

TBA

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: 11th Plasma Kinetics Working Group Meeting (2018)

We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set $Theta$ of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programming principle we link this non-linear expectation to a variational form of the Kolmogorov equation, where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in $Theta$. This non-linear affine process yields a tractable model for Knightian uncertainty, especially for modelling interest rates under ambiguity. We then develop an appropriate Ito-formula, the respective term-structure equations and study the non-linear versions of the Vasicek and the Cox-Ingersoll-Ross (CIR) model. Thereafter we introduce the non-linear Vasicek-CIR model. This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence the approach solves this modelling issue arising with negative interest rates. Joint work with Tolulope Fadina and Ariel Neufeld.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

In a joint work with Walter Schachermayer (still in progress), we investigate the optimal strategy of an economic agent trading a fractional asset in presence of transaction costs. A fascinating conjecture by us asserts that, contrary to the Bronwnian case, such an optimal trading would be fully discrete, only involving countably many trading times. What we can already prove is that only certain specific times, which we call "potential trading times", may involve trading, regardless of the agent's porfolio (this shall be explained more in detail). An idea towards our conjecture (though unsuccessful yet) would be to bound above the fractal dimension of the set of potential trading times. The nice point with this approach is that, contrary to the optimal strategy, this fractal dimension can be computed numerically: the goal of my talk will be to explain how one can do so. The method I propose involves quasi-stationary distributions, that is, killed Markov processes conditioned by long-time survival: which is rather surprising, as this concept has a priori nothing to do with fractal dimension ...

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

Motivated by recent advances in rough volatility modeling, we introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classica affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. Nonetheless, their Fourier-Laplace functionals admit exponential-affine representations in terms of solutions of associated deterministic integral equations, extending the well-known Riccati equations for classical affine diffusions. Our findings generalize and clarify recent results in the literature on rough volatility.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

We introduce a new method to price American options based on Chebyshev interpolation. The key advantage of this approach is that it allows to shift the model-dependent computations into an offline phase prior to the time-stepping. This leads to a highly efficient online phase. The model-dependent part can be solved with any computational method such as solving a PDE, using Fourier integration or Monte Carlo simulation.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

We will discuss non-exponential versions of well known limit theorems, specialising on the case of Brownian motion. The proofs will partially rely on the theory of BSDEs and their convex dual formulations, and an application to (stochastic) optimal transport will be provided.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

When we are ill, most of us would prefer to receive treatment that was supported by scientific evidence, rather than anecdotal tradition or superstition. When a nation's economy is ill, policy-makers turn to economists for advice, but how well is their advice supported by evidence? This talk critiques the value of economic theory in practice, and tries to suggest ways of increasing the practical relevance of the subject.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

Partial differential equations (PDEs) are among the most universal tools used in modelling problems in nature and man-made complex systems. For example, stochastic PDEs are a fundamental ingredient in models for nonlinear filtering problems in chemical engineering and weather forecasting, deterministic Schroedinger PDEs describe the wave function in a quantum physical system, deterministic Hamiltonian-Jacobi-Bellman PDEs are employed in operations research to describe optimal control problems where companys aim to minimise their costs, and deterministic Black-Scholes-type PDEs are also highly employed in portfolio optimization models as well as in state-of-the-art pricing and hedging models for financial derivatives. The PDEs appearing in such models are often high-dimensional as the number of dimensions, roughly speaking, corresponds to the number of all involved interacting substances, particles, resources, agents, or assets in the model. For instance, in the case of the above mentioned financial engineering models the dimensionality of the PDE often corresponds to the number of financial assets in the involved hedging portfolio. Such PDEs can typically not be solved explicitly and it is one of the most challenging tasks in applied mathematics to develop approximation algorithms which are able to approximatively compute solutions of high-dimensional PDEs. Nearly all approximation algorithms for PDEs in the literature suffer from the so-called "curse of dimensionality" in the sense that the number of required computational operations of the approximation algorithm to achieve a given approximation accuracy grows exponentially in the dimension of the considered PDE. With such algorithms it is impossible to approximatively compute solutions of high-dimensional PDEs even when the fastest currently available computers are used. In this talk we introduce of a class of new stochastic approximation algorithms for high-dimensional nonlinear PDEs. We prove that these algorithms do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and we thereby prove, for the first time, that a general semilinear parabolic PDE with a nonlinearity depending on the PDE solutiothe approximation algorithm to achieve a given approximation accuracy grows exponentially in the dimension of the considered PDE.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

A market of financial securities with restricted participation is considered. Agents are heterogeneous in beliefs, risk tolerance and endowments, and may not have access to the trade of all securities. The market is assumed thin: agents may influence the market and strategically trade against their price impacts. Existence and uniqueness of the equilibrium is shown, and an efficient algorithm is provided to numerically obtain the equilibrium prices and allocations given market’s inputs. (Based on joint work with M. Anthropelos.)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

Probability-valued jump-diffusions provide useful approximations of large stochastic systems in finance, such as large sets of equity returns, or particle systems with mean-field interaction. The dynamics of a probability-valued jump-diffusion is governed by an integro-differential operator of Levy type, expressed using a notion of derivative that is well-known from the superprocesses literature. General and easy-to-use existence criteria for probability-valued jump-diffusions are derived using new optimality conditions for functions of probability arguments. In general, we consider the space of probability measures as endowed with the topology of weak convergence. For jump-diffusions taking value on a specific subset of the probability measures, it can however be useful to work with a stronger notion of convergence. Think for instance at the well-known Wasserstein spaces. This change of topology permits to include in the theory a larger class of generators, and hence, a larger class of probability-valued jump-diffusions. We derive general and easy-to-use existence criteria for jump-diffusions valued in those spaces.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

In this talk I will explain what is a Variable Annuities (VA) contract and how we can find the pricing formula of VA when the financial market is hybrid in the sense introduced by Eberlein.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

We present an extension of the Furstenberg-Zimmer structural theory to the action of uncountable groups on not necessarily standard Borel probability spaces. Potential applications include Roth type results in uncountable groups. Based on ongoing work with Terence Tao.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

Insurance contracts are efficient risk management techniques to operate and reduce losses. However, very often, the underlying probability model for losses - on the basis of which premium is computed - is not completely known. Furthermore, in the case of extreme climatic events, the lack of data increases the epistemic uncertainty of the model. In this talk we propose a method to incorporate ambiguity into the design of an optimal insurance contract. Due to coverage limitations in this market, we focus on the limited stop-loss contract, given by $I(x)=min(max(x-d_1),d_2)$, with deductible $d_1$ and cap $d_2$. Therefore, we formulate an optimization problem for finding the optimal balance between the contract parameters that minimize some risk functional of the final wealth. To compensate for possible model misspecification, the optimal decision is taken with respect to a set of non-parametric models. The ambiguity set is built using a modified version of the well-known Wasserstein distance, which results to be more sensitive to deviations in the tail of distributions. The optimization problem is solved using a distributionally robust optimization setup. We examine the dependence of the objective function as well as the deductible and cap levels of the insurance contract on the tolerance level change. Numerical simulations illustrate the procedure.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

In this talk, we propose a novel approach to the modelling of multiple yield curves. Adopting the HJM philosophy, we model term structures of forward rate agreements (FRA) and OIS bonds. Our approach embeds most of the existing approaches and additionally allows for stochastic discontinuities. In particular, this last feature has an important motivation in interest rate markets, which are affected by political events and decisions occurring at predictable times. We study absence of arbitrage using results from the recent literature on large financial markets and discuss special cases and examples. This talk is based on joint work with Zorana Grbac, Sandrine Gümbel and Thorsten Schmidt.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)

I'll try in this talk to present the main ideas on zero-sum continuous time games where one of the two players has some private information (for instance when only one player observes a Brownian motion): how to formalize these games, the associated Hamilton-Jacobi-Isaacs-equation and the analyse of the optimal revelation in terms of an optimization problem over a set of martingales. In a second time I'll present the last developments in this area.

• Thematic program: Stochastics and Finance (2018/2019)
• Event: Stochastic Finance Workshop (2018)