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Related papers: Optimal stopping problem under random horizon

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We consider a general formulation of the random horizon Principal-Agent problem with a continuous payment and a lump-sum payment at termination. In the European version of the problem, the random horizon is chosen solely by the principal…

Optimization and Control · Mathematics 2022-02-11 Yiqing Lin , Zhenjie Ren , Nizar Touzi , Junjian Yang

In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable…

Mathematical Finance · Quantitative Finance 2024-01-12 Tahir Choulli , Emmanuel Lepinette

In the classical optimal stopping problem, a player is given a sequence of random variables $X_1\ldots X_n$ with known distributions. After observing the realization of $X_i$, the player can either accept the observed reward from $X_i$ and…

Discrete Mathematics · Computer Science 2020-07-24 Shipra Agrawal , Jay Sethuraman , Xingyu Zhang

We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from…

Optimization and Control · Mathematics 2015-03-18 Yongxin Chen , Tryphon Georgiou , Michele Pavon

We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…

Optimization and Control · Mathematics 2025-06-24 Václav E. Beneš , Georgy Gaitsgori , Ioannis Karatzas

In this paper we study optimal stopping problems with respect to distorted expectations of the form \begin{eqnarray*} \mathcal{E}(X)=\int_{-\infty}^{\infty} x\,dG(F_X(x)), \end{eqnarray*} where $F_X$ is the distribution function of $X$ and…

Optimization and Control · Mathematics 2015-06-16 Denis Belomestny , Volker Kraetschmer

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…

Probability · Mathematics 2020-12-07 Hugh Entwistle , Christopher Lustri , Georgy Sofronov

This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with…

Optimization and Control · Mathematics 2023-11-22 Giorgio Ferrari , Shihao Zhu

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…

Mathematical Finance · Quantitative Finance 2014-12-16 Denis Belomestny , Volker Kraetschmer

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…

Optimization and Control · Mathematics 2026-03-12 Jodi Dianetti , Giorgio Ferrari , Renyuan Xu

We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative…

Probability · Mathematics 2013-03-01 Magdalena Kobylanski , Marie-Claire Quenez

We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative L\'evy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first…

Mathematical Finance · Quantitative Finance 2018-08-10 Neofytos Rodosthenous , Hongzhong Zhang

In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We…

Probability · Mathematics 2019-08-21 Hanwu Li

In this paper, we study a stochastic linear-quadratic control problem with random coefficients and regime switching on a horizon $[0,T\wedge\tau]$, where $\tau$ is a given random jump time for the underlying state process and $T$ is a…

Optimization and Control · Mathematics 2022-01-19 Ying Hu , Xiaomin Shi , Zuo Quan Xu

We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…

Probability · Mathematics 2015-08-06 V. I. Arkin , A. D. Slastnikov

A multi-source quickest detection problem is considered. Assume there are two independent Poisson processes $X^{1}$ and $X^{2}$ with disorder times $\theta_{1}$ and $\theta_{2}$, respectively; that is, the intensities of $X^1$ and $X^2$…

Computational Engineering, Finance, and Science · Computer Science 2007-07-13 Erhan Bayraktar , H. Vincent Poor

We study the valuation of an American put option with a random time horizon given by the last exit time of the underlying asset from a fixed level. Since this random time is not a stopping time, the problem falls outside the classical…

Probability · Mathematics 2026-03-31 Zhuoshu Wu , Libo Li

We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…

Probability · Mathematics 2013-06-20 V. I. Arkin , A. D. Slastnikov

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…

Optimization and Control · Mathematics 2017-07-07 Erhan Bayraktar , Christopher W. Miller

We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…

Mathematical Finance · Quantitative Finance 2026-03-10 Anne Mackay , Marie-Claude Vachon