Related papers: An optimal stopping problem for fragmentation proc…
In this paper we study a representation problem first considered in a simpler version by Bank and El Karoui [2004]. A key ingredient to this problem is a random measure $\mu$ on the time axis which in the present paper is allowed to have…
It is shown that a certain functional of a branching process has representations in terms of both a maximisation problem and a minimisation problem. A consequence of these representation is that upper and lower bounds on the functional can…
We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time…
We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is…
We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…
We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process…
We give a stochastic model for the fragmentation phase of a snow avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by J. Bertoin. A fractal property of this…
A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekstr\"om, Lindberg and Tysk studied the problem of…
We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T , by minimizing an objective…
Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…