A Note on the Optimal Dividends Paid in a Foreign Currency

TL;DR

This paper analyzes an insurance company's dividend payout strategy in a foreign currency, modeling currency fluctuations with a Lévy process, and derives explicit formulas for optimal dividends under different payment restrictions.

Contribution

It provides explicit solutions for the optimal dividend payout strategy considering currency risk modeled by a Lévy process, extending previous models to foreign currency contexts.

Findings

Explicit formulas for the value function and optimal strategy.

Optimal strategies differ under restricted and unrestricted dividend payments.

Model incorporates currency fluctuations affecting dividend valuation.

Abstract

We consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are declared or paid in a foreign currency. The currency fluctuation is modelled as a L\'evy process. We consider both cases: restricted and unrestricted dividend payments. It turns out that the value function and the optimal strategy can be calculated explicitly.