Optimal Stopping Times with Different Information Levels and with Time Uncertainty

Chakrabarty, Arijit; Guo, Xin

doi:10.1142/9789814383585_0002

Cited by 4 publications

(10 citation statements)

References 30 publications

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“…Thanks to a result in [1], we show in the Appendix that there is no loss of generality in using stopping times from T t,T . That is, we obtain the same value in (2.4) as if we were using stopping times of the enlarged filtration (G t ) t≥0 , where…”

Section: Remark 22mentioning

confidence: 99%

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On the free boundary of an annuity purchase

Angelis

Stabile

2018

Finance Stoch

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It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies if the mortality force is a generic function of time and the subjective life expectancy of the investor differs from the objective one adopted by insurance companies to price annuities. In this paper, we address this problem by considering an individual who invests in a fund and has the option to convert the fund's value into an annuity at any time. We formulate the problem as a real option and perform a detailed probabilistic study of the optimal stopping boundary. Due to the generic time-dependence of the mortality force, our optimal stopping problem requires new solution methods to deal with nonmonotonic optimal boundaries.

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Section: Remark 22mentioning

confidence: 99%

“…Here we use an argument from [1] to confirm that we incur no loss of generality in optimising over T t,T instead of using stopping times with respect to (G t ) t≥0 , where…”

Section: Appendix A: Admissible Stopping Timesmentioning

confidence: 99%

On the free boundary of an annuity purchase

Angelis

Stabile

2018

Finance Stoch

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“…where S(y) = (p + y)/(1 − p), and the supremum is taken over stopping times with respect to the filtration generated by the Q-Brownian motion Z. compare [3], where ν is exponentially distributed with parameter λ(1 − p)/p. Thus, if u is a fixed point of J , i.e.…”

Section: The Building Block: An Optimal Stopping Problem Without Jumpsmentioning

confidence: 99%

Momentum liquidation under partial information

Ekström

Vannestål

2016

J. Appl. Probab.

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Momentum is the notion that an asset that has performed well in the past will continue to do so for some period. We study the optimal liquidation strategy for a momentum trade in a setting where the drift of the asset drops from a high value to a smaller one at some random change-point. This change-point is not directly observable for the trader, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. Comparisons with existing results for momentum trading under incomplete information show that the assumption that the disappearance of the momentum effect is triggered by observable external shocks significantly improves the optimal strategy.

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“…In some applications, however, information is a scarce resource, and the stopper then needs to base her decision only on the information available upon stopping. We study stopping problems of the type sup τ E g(τ, X τ , θ)1 {τ <γ } + h(γ, X γ , θ)1 {γ ≤τ } , (1) where X is a diffusion process; here g and h are given functions representing the payoff if stopping occurs before or after the random time horizon γ , respectively, and θ is a Bernoulli random variable representing the unknown state. This unknown state may influence the drift of the diffusion process X, the distribution of the random horizon γ and the payoff functions g and h.…”

Section: Introductionmentioning

confidence: 99%

“…The related literature includes optimal stopping for regime-switching models (see [12] and [23]), studies of models containing change points [9,13], a study allowing for an arbitrary distribution of the unknown state [6], problems of stochastic control [16] and singular control [2], and stochastic games [3] under incomplete information. Stopping problems with a random time horizon are studied in, for example, [1] and [17], where the authors consider models with a random finite time horizon but with state-independent distributions; for a study with a state-dependent random horizon, see [8].…”

Section: Introductionmentioning

confidence: 99%

Stopping problems with an unknown state

Ekström

Wang

2023

J. Appl. Probab.

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We extend the classical setting of an optimal stopping problem under full information to include problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, standard filtering theory can be employed to embed the problem in a Markovian framework with one additional state variable representing the posterior of the unknown state. We provide a convenient formulation of this Markovian problem, based on a measure change technique that decouples the underlying process from the new state variable. Moreover, we show by means of several novel examples that this reduced formulation can be used to solve problems explicitly.

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Optimal Stopping Times with Different Information Levels and with Time Uncertainty

Cited by 4 publications

References 30 publications

On the free boundary of an annuity purchase

On the free boundary of an annuity purchase

Momentum liquidation under partial information

Stopping problems with an unknown state

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