On the surplus management of funds with assets and liabilities in presence of solvency requirements

Benjamin Avanzi, Ping Chen, Lars Frederik Brandt Henriksen and Bernard Wong

Papers from arXiv.org

Abstract: In this paper we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu (2003). We determine what dividend strategy maximises the expected present value of dividends until ruin in two cases: (i) when shareholders won't cover surplus shortfalls and a solvency constraint (as in Paulsen, 2003) is consequently imposed, and (ii) when shareholders are always to fund any capital deficiency with capital (asset) injections. In the latter case, ruin will never occur and the objective is to maximise the difference between dividends and capital injections. Developing and using appropriate verification lemmas, we show that the optimal dividend strategy is, in both cases, of barrier type. Both value functions are derived in closed form. Furthermore, the barrier is defined on the ratio of assets to liabilities, which mimics some of the dividend strategies that can be observed in practice by insurance companies. Existence and uniqueness of the optimal strategies are shown. Results are illustrated.

Date: 2022-03, Revised 2022-08
New Economics Papers: this item is included in nep-ias and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2203.05139

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