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- W1951006475 abstract "We consider an insurance company in the case when the premium rate is a bounded non-negative random function ct and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility σ>0. If β≔2a/σ2-1>0 we find exact the asymptotic upper and lower bounds for the ruin probability Ψ(u) as the initial endowment u tends to infinity, i.e. we show that C*u-β⩽Ψ(u)⩽C*u-β for sufficiently large u. Moreover if ct=c*eγt with γ⩽0 we find the exact asymptotics of the ruin probability, namely Ψ(u)∼u-β. If β⩽0, we show that Ψ(u)=1 for any u⩾0." @default.
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- W1951006475 date "2006-02-01" @default.
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- W1951006475 title "Ruin probability in the presence of risky investments" @default.
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- W1951006475 doi "https://doi.org/10.1016/j.spa.2005.09.006" @default.
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