Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (1): 137-147.

• Articles • Previous Articles     Next Articles

Optimal Proportional Reinsurance and Investment with Transaction Costs and Liability

 ZHANG Xin-Li, SUN Wen-Yu   

  1. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046)
  • Received:2010-06-15 Revised:2011-07-04 Online:2012-02-25 Published:2012-02-25
  • Supported by:

    国家自然科学基金(10871098)、江苏省自然科学基金(BK2009397)和江苏省博士后科研基金 (1001073C)资助

Abstract:

In this paper, the authorsconsidera problem ofoptimal reinsuranceand investment with multiple risky assets and a liability for an insurance company whose surplus is governed by a linear diffusion. The insurance company’s risk can be reduced through reinsurance, while in addition the company invests its surplus in a financial market with one risk-free asset and m risky assets. The risky assets’ prices are governed by geometric Brownian motions while the liability evolves according to a Brownian motion with drift. The correlations between the risky assets and the liability are considered. The transaction costs produced during the investmentaretaken into account. Te authors considerthe optimization problemof maximizing the expected exponential utility of terminal wealth and solve it by using the corresponding Hamilton-Jacobi-Bellman(HJB) equation. Explicit expression for the optimal value function and the corresponding optimal strategies are obtained.

Key words: Hamilton-Jacobi-Bellman equation, Liability, Proportional reinsurance, Transac-tion costs

CLC Number: 

  • 90B50
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