Related papers: Optimal Stopping for Non-linear Expectations
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
We study an infinite horizon optimal stopping problem which arises naturally in the optimal timing of a firm/project sale or in the valuation of natural resources: the functional to be maximised is a sum of a discounted running reward and a…
In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…
In a classical optimal stopping problem in continuous time, the agent can choose any stopping time without constraint. Dupuis and Wang (Optimal stopping with random intervention times, Advances in Applied Probability, 34, 141--157, 2002)…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
Bruss's odds theorem \cite{Bruss1} addresses the problem of determining the optimal stopping time for sequences of independent indicator functions. In this note, we derive upper and lower bounds for the success probability under the optimal…
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…
Sellers in online markets face the challenge of determining the right time to sell in view of uncertain future offers. Classical stopping theory assumes that sellers have full knowledge of the value distributions, and leverage this…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject…
This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem, which has its…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…