RESEARCH ARTICLE

Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information

  • Jie XIONG , 1 ,
  • Shuaiqi ZHANG , 2,3 ,
  • Hui ZHAO 4 ,
  • Xihuan ZENG 5
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  • 1. Department of Mathematics, FST, University of Macau, Macau, China
  • 2. School of Economics and Commerce, Guangdong University of Technology, Guangzhou 510520, China
  • 3. Department of Statistics, Hebei University of Technology, Tianjin 300401, China
  • 4. Department of Mathematics, Tianjin University, Tianjin 300072, China
  • 5. Institute of Business Administration, University of Macau, Macau, China

Received date: 19 Feb 2014

Accepted date: 09 Jun 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.

Cite this article

Jie XIONG , Shuaiqi ZHANG , Hui ZHAO , Xihuan ZENG . Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 965 -982 . DOI: 10.1007/s11464-014-0403-5

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