An Introduction to Mathematical Risk Theory

adjustment coefficient aggregate claims applied approximation assume assumption C₁ chapter claim amount distribution compound Poisson distribution compound Poisson process conditional distribution Consider convergence counting process defined denote derivative discussed dividend Edgeworth Edgeworth series Esscher transform example 1.2 Example 3.1 expected number exponential claim amounts exponential distribution exponential principle follows formula function gamma gamma distribution given independent inequality initial surplus integral intensity of frequency interpretation interval Kolmogorov's inequality Laplace transform Markov process martingale with respect mean value principle number of claims Observe obtained optimal P₁ Partition Method Poisson parameter premium principle probability of ruin random variable random walk reinsurance renewal equation result right side risk exchange risk theory ruin theory S₁ satisfies say with parameter security loading solution stochastic process stop-loss premiums submartingale Suppose T₁ Taylor series tion Typical Sample Path Upper Bounds variance X₁ Y₁ yes yes