Optimal loss-carry-forward taxation for the Lévy risk model

Wenyuan Wang and Yijun Hu

Insurance: Mathematics and Economics, 2012, vol. 50, issue 1, 121-130

Abstract: In the spirit of Albrecher and Hipp (2007), Albrecher et al. (2008b) and Kyprianou and Zhou (2009), we consider the reserve process of an insurance company which is governed by Rtπ=Xt−∫0tγπ(Sσ)dSσ, where X is a spectrally negative Lévy process with the usual exclusion of negative subordinator or deterministic drift, St:=max0≤σ≤tXσ the running supremum of X, and γπ(St) the rate of loss-carry-forward tax at time t which is subject to the taxation allocation policy π and is a function of St. The objective is to find the optimal policy which maximizes the total (discounted) taxation pay-out: Ex∫0τπe−ctγπ(St)dSt, where Ex and τπ refer to the expectation corresponding to the law of X such that X0=x, and the time of ruin, respectively. With the scale function of X denoted by Wc(x) and γπ(⋅) allowed to vary in [α,β](0≤α≤β<1), two situations are considered. (a)∫0∞(Wc(y))1−11−β(Wc)″(y)[(Wc)′(y)]2dy≥0. It is shown that the optimal strategy is to always pay tax at the maximum rate β.(b)∫0∞(Wc(y))1−11−β(Wc)″(y)[(Wc)′(y)]2dy<0. Then the optimal strategy prescribes to pay tax at the smallest rate α when the reserve is below some critical level u0, and to pay at the maximum rate β when the reserve is above u0.

Keywords: Spectrally negative Lévy process; Stochastic control; HJB equation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:50:y:2012:i:1:p:121-130

DOI: 10.1016/j.insmatheco.2011.10.011

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