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The problem of determining optimal retention levels for a non-life portfolio consisting of a number of independent sub-portfolios was first discussed by de Finetti (1946). He considered retention levels to be optimal if they minimized the variance of the insurer's profit from the portfolio subject to the constraint of a fixed level of expected profit. In this presentation the criterion for optimality is minimizing the probability of ruin, either in discrete or continuous time. The author investigates this problem through a series of case studies based on a real portfolio.
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Counting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and sem
Yushkevich can also be applied to certain models where control of the flow is possible. The method consists in a transformation to a model without control of the flow by a kind of time change.
By taking the relevant expectations, the model yields a complete initial term structure for the continuum of maturities, endogenously interpolating between the observed data. Thus it is more parsimonious in its assumptions in the sense that there is no need for an exogenous interpolation rule and th