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Moment-constrained optimal dividends: precommitment and consistent planning

Part of: Markov processes Stochastic systems and control Mathematical finance Game theory

Published online by Cambridge University Press:  06 June 2022

Sören Christensen  and
Kristoffer Lindensjö Open the ORCID record for Kristoffer Lindensjö [Opens in a new window]
Sören Christensen*
Affiliation:
Kiel University
Kristoffer Lindensjö*
Affiliation:
Stockholm University
*
*Postal address: Department of Mathematics, Christian-Albrechts-University Kiel, Heinrich-Hecht-Platz 6, 24118 Kiel, Germany. Email address: christensen@math.uni-kiel.de
**Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden. Email address: kristoffer.lindensjo@math.su.se
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Abstract

A moment constraint that limits the number of dividends in an optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz’s consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame-perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion.

Keywords

Constrained stochastic controlstochastic impulse controlStrotz’s consistent planningsubgame-perfect Nash equilibriumtime-inconsistency

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 91A15: Stochastic games 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 404 - 432
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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