Graduate Thesis Or Dissertation
 

Ruin theory under uncertain investments

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/9593tz38v

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  • An insurance company, having an initial capital u, receives premiums continuously and pays claims of random sizes at random times. A classical result states that if the rate of premium, c, exceeds the average of the claims paid per unit time, ⋋μ, then the ruin probability decays exponentially fast as u → ∞. However, if the insurance company invests in a risky asset whose price follows a geometric Brownian motion with drift a and volatility σ > 0, it is known that the probability of ruin decays at best algebraically, under a specific model for claim size distribution. In this thesis, the result is shown to be valid for claim size distributions having moment generating functions defined in a neighborhood of the origin.
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