moż e mi to ktoś na polski strzelić?
: 09 mar 2009, 1:12
We use the exponential martingale: for a sequence of i.i.d random variables with existing moment generating function, i.e. AA for some AA; one check that the sequence AA is a martingale AA. Abowe we assumed AA to be normally distributed, so AA. Now the event of bankruptcy occurs if the wealth of the insurance company is negative, so define the stopping time AA.Since for any AA the stopping time AA is bounded and by AA is a martingale, we can use AA stopping principle. Now AA where we used the positivity of the second expression, and the fact that from AA and AA it follows that AA. Combining the last two expressions, we find AA . Since the inequality holds for all AA follows.