Optimal implementation delay of taxation with trade-off for L\'{e}vy risk Processes

TL;DR

This paper studies optimal timing strategies for implementing taxation in insurance risk models driven by spectrally negative Lévy processes, balancing tax revenue, terminal value, and capital injection costs.

Contribution

It introduces two new models for optimal tax implementation delay considering terminal value and capital injections in Lévy risk processes.

Findings

Derived explicit formulas for optimal implementation levels

Provided numerical examples illustrating the models' applications

Analyzed trade-offs between tax timing, terminal value, and capital costs

Abstract

In this paper we consider two problems on optimal implementation delay of taxation with trade-off for spectrally negative L\'{e}vy insurance risk processes. In the first case, we assume that an insurance company starts to pay tax when its surplus reaches a certain level $b$ and at the termination time of the business there is a terminal value incurred to the company. The total expected discounted value of tax payments plus the terminal value is maximized to obtain the optimal implementation level $b^*$. In the second case, the company still pays tax subject to an implementation level $a$ but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the capital injection costs is maximized to obtain the optimal implementation level $a^*$. Numerical examples are also given to illustrate the main results in this paper.