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hw8 - IEOR 4404 Simulation Prof Mariana Olvera-Cravioto...

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IEOR 4404 Assignment #8 Simulation October 26, 2006 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #8 – due November 3rd, 2006 1. (From Ross) Suppose in the insurance risk model presented in class that, conditional on the event that the firm’s capital goes negative before time T , we are also interested in the time at which it becomes negative and the amount of the shortfall. Explain how we an use the given simulation methodology to obtain relevant data. 2. (From Ross) A system experiences shocks that occur in accordance with a Poisson process having a rate of 1/hour. Each shock has a certain amount of damage associated with it. These damages are assumed to be independent random variables (which are also independent of the times at which the shocks occur), having the common density function f ( x ) = xe - x , x > 0 Damages dissipate in time at an exponential rate α —that is, a shock whose initial damage is x will have remaining damage value xe - as at time s after it occurs. In addition, the damage values are cumulative. Thus, for example, if by time
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