Discrete Time Risk Models With Random Premiums
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Date
2018-04-27Author
Smith, Llewellyn Hillyer
0000-0003-1845-1144
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Over the past century insurance companies relied to a large extent on the continuous time Mathematical Risk Model proposed by Lundberg, known for its ability to estimate the probability of ruin(capital reserve falling below zero), given the initial capital, linear premium rate and cumulative random size claims occurring at random times. In this Dissertation we introduce a discrete time risk model that allows random premiums, and derive the estimates of the ruin probabilities on both finite and infinite time horizons. Tools applied are drawn from modern probability and include,Martingales, Invariance Principle for Brownian motions, and Large Deviation Principle for the asymptotics of rare events. Our considerations can be dubbed “end of the day model”, as ruin is neither declared nor acted upon when it falls between successive discrete times.