Moment constrained optimal dividends: precommitment \&amp; consistent planning

Christensen, Sören; Lindensjö, Kristoffer

doi:10.48550/arxiv.1909.10749

Cited by 3 publications

(3 citation statements)

References 39 publications

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“…[20] studies a framework under general preference structure. A version of the classical dividend problem with a time-inconsistent restriction is studied in [14] using both the precommitment and consistent planning approach. Further references to the literature are found throughout the paper.…”

Section: Time-inconsistency In Economics and Related Literaturementioning

confidence: 99%

Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application

Christensen,

Lindensjö

2019

Preprint

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For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are timeinconsistent due to the consideration of a non-linear function of an expected reward. We consider pure and mixed stopping strategies and a (subgame perfect Nash) equilibrium. We provide different necessary and sufficient equilibrium conditions including a verification theorem. Using a fixed point argument we provide equilibrium existence results. We adapt and study the notion of the myopic adjustment process and introduce different kinds of equilibrium stability. We show that neither existence nor uniqueness of equilibria should generally be expected. The developed theory is applied to a mean-variance problem and a variance problem.

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Section: Time-inconsistency In Economics and Related Literaturementioning

confidence: 99%

Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application

Christensen,

Lindensjö

2019

Preprint

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“…[13] study a discrete-time Markov chain stopping problem and propose a definition of sub-game perfect Nash equilibrium for which necessary and sufficient equilibrium conditions are derived, and an equilibrium existence result is obtained. They extend their study to the continuous setting by considering diffusion dynamics in [14], and study in [12] a moment constrained version of the optimal dividend problem for which both the pre-committed and sub-game perfect solutions are studied. Independently, [4] studied a continuous Markov chain process and propose another notion of equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents

Hernández¹,

Possamaï²

2020

Preprint

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We develop a theory for continuous-time non-Markovian stochastic control problems which are inherently time-inconsistent. Their distinguishing feature is that the classical Bellman optimality principle no longer holds. Our formulation is cast within the framework of a controlled non-Markovian forward stochastic differential equation, and a general objective functional setting. We adopt a game-theoretic approach to study such problems, meaning that we seek for sub-game perfect Nash equilibrium points. As a first novelty of this work, we introduce and motivate a new definition of equilibrium that allows us to establish rigorously an extended dynamic programming principle, in the same spirit as in the classical theory. This in turn allows us to introduce a system of backward stochastic differential equations analogous to the classical HJB equation. We prove that this system is fundamental, in the sense that its well-posedness is both necessary and sufficient to characterise the value function and equilibria. As a final step we provide an existence and uniqueness result. Some examples and extensions of our results are also presented.

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“…and the optimal policy is to reflect the state process X at a barrier consisting of the inflection point b * , with an immediate dividend of x − b * in case x > b * ; see[17, Theorem 4.3] and[6, Proposition 2.6].…”

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confidence: 99%

De Finetti's control problem with competition

Ekström¹,

Lindensjö²

2021

Preprint

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We investigate the effects of competition in a problem of resource extraction from a common source with diffusive dynamics. In the symmetric version with identical extraction rates we prove the existence of a Nash equilibrium where the strategies are of threshold type, and we characterize the equilibrium threshold. Moreover, we show that increased competition leads to lower extraction thresholds and smaller equilibrium values. For the asymmetric version, where each agent has an individual extraction rate, we provide the existence of an equilibrium in threshold strategies, and we show that the corresponding thresholds are ordered in the same way as the extraction rates.

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Moment constrained optimal dividends: precommitment \& consistent planning

Cited by 3 publications

References 39 publications

Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application

Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application

Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents

De Finetti's control problem with competition

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