An Introduction to Mathematical Risk Theory

according additional aggregate claims applied approximation assume assumption Bounds calculation called chapter claim amount distribution compound Poisson distribution condition Consider constant continuous convergence corresponding counting process decision defined denote derived Differentiating discussed equals equation Esscher event example exchangeable expected expression figure Finally follows formula frequency function gamma given holds implies important increments independent individual inequality integral interest interpretation interval known leads limit martingale means method negative normal Note Observe obtained occurs parameter particular Poisson parameter Poisson process positive possible premium present principle probability proof random variable random walk result risk risk theory ruin sample path satisfies sequence solution stochastic process Suppose surplus tion transform unit utility valid variance weighted X₁ yields zero