Related papers: Spanning Tests for Markowitz Stochastic Dominance
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
We consider the investor who doesn't trade shares of his portfolio. The investor only observes the current trades made in the market with his securities to estimate the current return, variance, and risks of his unchanged portfolio. We show…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Structural results impose sufficient conditions on the model parameters of a Markov decision process (MDP) so that the optimal policy is an increasing function of the underlying state. The classical assumptions for MDP structural results…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regions. The spectrum as a whole has also been analysed,…
This paper proposes a nonparametric test for $m$th-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The…
Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at…
In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process…
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
Model Predictive Control (MPC) is well understood in the deterministic setting, yet rigorous stability and performance guarantees for stochastic MPC remain limited to the consideration of terminal constraints and penalties. In contrast,…
Unnormalized probability distributions are central to modeling complex physical systems across various scientific domains. Traditional sampling methods, such as Markov Chain Monte Carlo (MCMC), often suffer from slow convergence, critical…
The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…