產險公司保險槓桿與股利之動態決策

Dynamic Insurance Leverage and Dividend Decisions for a Property-Liability Insurance Firm

產險公司的財務決策中，保險槓桿及股利發放率是攸關公司股東利益及受監理者關心的兩個重要決策。但是在過去文獻中它們很少同時以用連續時間動態規劃的方法來求分析。本文以一產險公司的淨值擴散過程為基礎，假設其目標是極大化股東於計劃時間內所獲期望股利現值總和，同時也極小化期望破產成本之現值。我們藉由隨機控制的方法來探討此二共同最適決策。在一些假設條件下、包括連續控制或隨機破產的情況下，我們分別求取封閉解。我們更進一步利用數值方法來解除一些條件限制以求得最適決策。本文之結果可以作為產險公司資本結構動態決策的理論模型基礎。

In the context of risk management process, a firm needs to control a variety of operational and financial decisions. Two critical decisions to be made for a property and liability (P/L) insurance firm are the amount of insurance to sell at market and the amount of dividend compensation to be afforded equity owners. In this paper, we consider a P/L insurer whose net worth is modeled by a diffusion process, and its objective is to maximize the expected discounted dividend payouts to the shareholders as well as minimize the expected discounted cost of insolvency. By using the technique of continuous-time stochastic control, we solve the optimal joint decisions of insurance leverage and dividend payout rate. Our analysis is carried out under the assumptions of continuous control, as well as random planning time. With some assumptions, we show their close-form solutions. Finally, the numerical results using Markov chain numerical approximation are also illustrated to relieve impractical presumptions.