Related papers: General Optimal Stopping with Linear Costs
In this Note we study optimal stopping problems for strong Markov processes and affine functions. We give a justification of the Snell envelope form using standard results of optimal stopping. We also justify the convexity of the value…
In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost. In our previous work, we have shown that by utilizing…
We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a…
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…
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 consider the optimal stopping problem for a Gauss-Markov process conditioned to adopt a prescribed terminal distribution. By applying a time-space transformation, we show it is equivalent to stopping a Brownian bridge pinned at a random…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
We study a mathematical model motivated by the support/resistance line method in technical analysis where the underlying stock price transitions between three states of nature in a path-dependent manner. For optimal stopping problems with…
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
We study the Lagrangian formulation of a class of the Monge-Kantorovich optimal transportation problem. It can be considered a stochastic optimal transportation problem for absolutely continuous stochastic processes. A cost function and…
This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost function. We develop an approach to track the optimal solution with a bounded error. Unlike the…
The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…
Drawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure) and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with general drawdown times, which…
We study dynamical optimal transport of discrete time systems (dDOT) with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting…
In this paper, we study a continuous-time discounted jump Markov decision process with both controlled actions and observations. The observation is only available for a discrete set of time instances. At each time of observation, one has to…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…