I will review some recent results on optimal stopping and zero-sum Dynkin games problems for time-inconsistent models including recursive utility functions of mean-field type.
We consider the finite horizon risk-sensitive control problem for a system driven by a standard Brownian motion. We control the system only through the drift, the control set is unbounded, and the cost/reward function is superlinear with respect to the control variable. To solve the problem, we use the HJB theory and prove that the associated PDE admits a classical ($C^{2,1}$) solution.
Impulse control provides a versatile framework for applying discrete-type interventions in continuous-time phenomena. This type of control can be applied e.g. to design foreign exchange intervention policies, specify optimal harvesting schemes, and model portfolios with transaction costs. In this talk we will discuss a compact domain approximation of the long-run impulse control problem for...
We investigate the benefits of relating reinforcement learning (RL) with risk-sensitive control. Our starting point is the duality between free energy and relative entropy, see e.g. Dai Pra et al. (1996). It establishes an equivalence between risk-sensitive control and standard stochastic control problems with an entropy regularization term.
This approach has two major advantages:
i) it...
In this talk we will consider the problem of discrete-time risk-sensitive portfolio optimization over a long time horizon. In particular, the relationship between ergodic assumptions and the existence of a solution to a suitable Bellman equation will be discussed. This will include various portfolio optimisation frameworks linked to i.i.d. settings, the presence of proportional transaction...
In the talk we consider discrete time financial markets with concave transaction costs. This means that bid and ask prices depend on the volume of transaction in such a way that when we buy more assets we pay smaller (proportionally) transaction costs, while when we sell more assets we pay less for proportional transaction costs. Such situation appears usually on currency markets and real...
A Rosenblatt measure denotes the measure for a Rosenblatt process that is a non-Gaussian process that can be explicitly described as a product of two Wiener-Itô stochastic integrals with suitable singular kernels. These Rosenblatt processes have a useful stochastic calculus that includes an explicit change of variables formula. Given the usefulness of absolute continuity for Wiener measures,...
In 2017, the US National Science Foundation (NSF) announced 10 Big Ideas for Future Investment. These research ideas, such as ”Harnessing the Data Revolution” or ”Future of Work at the Human Technology Frontier”, all require expertise from multiple disciplines to come together to address specific problems that are important in our society. One of ideas, ”Growing Convergence Research” is...
In the talk for discrete time controlled Markov processes dependence of the long run functionals: average reward per unit time and risk sensitive, with respect to Markov controls, functions in the functional and risk factor (in the case of risk sensitive functionals) will be studied. It is shown that under nice ergodic assumptions we have suitable continuity properties. Such properties justify...
Let $(\Omega,\mathcal F,P)$ be a complete probability space and $\mathbb F:=(\mathcal F_t)$ be a filtration on $(\Omega,\mathcal F,P)$ satisfying usual conditions. Let $T>0$, $\nu$ be a natural number, and $\xi$ be an $\mathbb R^\nu$-valued $\mathcal F_T$-adapted random vector. We shall present the existence results for the following system of quadratic growth (with respect to $M$) ...
In this talk we study the problem of (online) forecasting general stochastic processes using a path-dependent (PD) extension of the Neural Jump ODE (NJ-ODE) framework. While NJ-ODE was the first framework to establish convergence guarantees for the prediction of irregularly observed time series, these results were limited to data stemming from It\^o-diffusions with complete observations, in...
Randomization improves the rate of convergence of numerical schemes for ordinary differential equations. In this talk, we will present error bounds and discuss optimality (in the Information-Based Complexity sense) for selected randomized ODE solvers. Error analysis will be performed assuming low regularity of the right-hand side function (local Holder and Lipschitz continuity in time and...
This work emphasizes the transformative potential of leveraging large-scale multimodal data archives in neuroinformatics research, particularly focusing on electrophysiology and neuroimaging datasets. By employing rigorous standardization and harmonization methodologies alongside state-of-the-art AI tools, these archives enable novel scientific discoveries across various brain disorders and...
Reliable simulation models are crucial in virtual engineering processes. Typically, the system of differential equations in these models is rather well known. However, the development of new product classes requires new parametrizations of the system. This often leads to vast experimental programs needed to acquire all necessary data to determine relevant parameters. The choice of experiments,...
