Optimising dividends and consumption under an exponential CIR as a discount factor

Julia Eisenberg () and Yuliya Mishura
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Julia Eisenberg: TU Wien
Yuliya Mishura: Taras Shevchenko National University of Kyiv

Mathematical Methods of Operations Research, 2020, vol. 92, issue 2, No 3, 285-309

Abstract: Abstract We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spending/dividend payments under a discounting factor given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the value function. For the Brownian motion case, we are able to show that for a special parameter choice the optimal strategy is a constant-barrier strategy.

Keywords: Hamilton–Jacobi–Bellman equation; Cox–Ingersoll–Ross process; Dividends; Brownian risk model; Consumption; Primary 93E20; Secondary 91B42; 91B30; 60H30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-020-00714-w

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