Suboptimal Control of Dividends under Exponential Utility



Eisenberg, Julia and Krühner, Paul
Suboptimal Control of Dividends under Exponential Utility.

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Abstract

We consider an insurance company modelling its surplus process by a Brownian motion with drift. Our target is to maximise the expected exponential utility of discounted dividend payments, given that the dividend rates are bounded by some constant. The utility function destroys the linearity and the time homogeneity of the considered problem. The value function depends not only on the surplus, but also on time. Numerical considerations suggest that the optimal strategy, if it exists, is of a barrier type with a non-linear barrier. In the related article by granditz et al., it has been observed that standard numerical methods break down in certain parameter cases and no close form solution has been found. For these reasons, we offer a new method allowing to estimate the distance of an arbitrary smooth enough function to the value function. Applying this method, we investigate the goodness of the most obvious suboptimal strategies - payout on the maximal rate, and constant barrier strategies - by measuring the distance of its performance function to the value function.

Item Type: Article
Uncontrolled Keywords: q-fin.RM, q-fin.RM, math.PR, 93E20, 91B30, 60H30
Depositing User: Symplectic Admin
Date Deposited: 12 Sep 2018 10:49
Last Modified: 18 Nov 2019 15:10
Open Access URL: http://arxiv.org/abs/1809.01983v1
Related URLs:
URI: http://livrepository.liverpool.ac.uk/id/eprint/3026104
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