English
Related papers

Related papers: Stability of Time-inconsistent Stopping for One-di…

200 papers

We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…

Probability · Mathematics 2024-05-28 Tiziano De Angelis , Damien Lamberton

For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…

Optimization and Control · Mathematics 2020-01-23 Sören Christensen , Kristoffer Lindensjö

Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for…

Optimization and Control · Mathematics 2017-03-13 Yu-Jui Huang , Adrien Nguyen-Huu

A finite horizon optimal stopping problem for an infinite dimensional diffusion $X$ is analyzed by means of variational techniques. The diffusion is driven by a SDE on a Hilbert space $\mathcal{H}$ with a non-linear diffusion coefficient…

Optimization and Control · Mathematics 2015-02-03 M. B. Chiarolla , T. De Angelis

We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…

Probability · Mathematics 2024-11-20 Takuji Arai , Masahiko Takenaka

For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function $V(\cdot)$ induced by all mild equilibria…

Optimization and Control · Mathematics 2024-12-30 Erhan Bayraktar , Zhenhua Wang , Zhou Zhou

The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…

Probability · Mathematics 2021-08-02 Philip Ernst , Hongwei Mei

We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function…

Probability · Mathematics 2014-01-13 Damien Lamberton , Mihail Zervos

This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…

Probability · Mathematics 2024-12-31 Idris Kharroubi , Antonio Ocello

We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0,\infty],…

Probability · Mathematics 2007-05-23 Paul Dupuis , Hui Wang

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…

Mathematical Finance · Quantitative Finance 2021-07-15 Yu-Jui Huang , Xiang Yu

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

This paper studies a central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude…

Mathematical Finance · Quantitative Finance 2025-10-15 Shuoqing Deng , Xiang Yu , Jiacheng Zhang

In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear diffusion in a bounded interval of the real line. In…

Analysis of PDEs · Mathematics 2025-09-10 Alessandro Alla , Alessandra De Luca , Raffaele Folino , Marta Strani

A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…

Optimization and Control · Mathematics 2020-01-23 Sören Christensen , Kristoffer Lindensjö

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

We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies…

Mathematical Finance · Quantitative Finance 2021-07-15 Yu-Jui Huang , Adrien Nguyen-Huu , Xun Yu Zhou

In this paper we provide detailed information about the instability of equilibrium solutions of a nonlinear family of localized reaction-difussion equations in dimensione one. Beyond we provide explicit formulas to the equilibrium…

Analysis of PDEs · Mathematics 2017-07-25 César Adolfo Hernández Melo , Edgar Yesid Mayorga Lancheros

We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…

Optimization and Control · Mathematics 2018-03-12 Luis H. R. Alvarez E.

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…

Optimization and Control · Mathematics 2018-12-05 Sören Christensen , Kristoffer Lindensjö