An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case

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• 作者：Peter Grandits
• 关键词：Optimal investment ; Ruin probabilities ; Integro ; differential equations
• 刊名：Applied Mathematics and Optimization
• 出版年：2004
• 出版时间：June 2004
• 年：2004
• 卷：50
• 期：1
• 页码：1-20
• 全文大小：193 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Systems Theory and Control
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  
• 出版者：Springer New York
• ISSN：1432-0606

文摘

We consider ruin probabilities for an insurance company, which canalso invest in the stock market. The risk process is modeled by a compound Poissonprocess and the stock price by geometric Brownian motion. We show that if the tailsof the claims are light tailed, then the optimal strategy is asymptotically given byholding a constant $-value in the stock position. Furthermore, we show that a kind ofCramér–Lundberg approximation holds for the minimal ruin probability. Everythingis shown under assumptions, which are analogous to the assumptions in the case of theclassical Cramér–Lundberg approximation without investment.