886 research outputs found
Ruin models with investment income
This survey treats the problem of ruin in a risk model when assets earn
investment income. In addition to a general presentation of the problem, topics
covered are a presentation of the relevant integro-differential equations,
exact and numerical solutions, asymptotic results, bounds on the ruin
probability and also the possibility of minimizing the ruin probability by
investment and possibly reinsurance control. The main emphasis is on continuous
time models, but discrete time models are also covered. A fairly extensive list
of references is provided, particularly of papers published after 1998. For
more references to papers published before that, the reader can consult [47].Comment: Published in at http://dx.doi.org/10.1214/08-PS134 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Ruin probabilities in a finite-horizon risk model with investment and reinsurance
A finite horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Obtaining explicit optimal solutions for the minimizing ruin probability problem is a difficult task. Therefore, we consider an alternative method commonly used in ruin theory, which consists in deriving inequalities that can be used to obtain upper bounds for the ruin probabilities and then choose the control to minimize the bound. We finally specialize our results to the particular, but relevant, case of exponentially distributed claims and compare for this case our bounds with the classical Lundberg bound.Risk process, Reinsurance and investment, Lundberg’s inequality, 91B30, 93E20, 60J28
Discrete analysis of dividend payments in a non-life insurance portfolio
The process of free reserves in a non-life insurance portfolio as defined in the classical model of risk theory is modified by the introduction of dividend policies that set maximum levels for the accumulation of reserves. The first part of the work formulates the quantification of the dividend payments via the expectation of their current value under different hypotheses. The second part presents a solution based on a system of linear equations for discrete dividend payments in the case of a constant dividend barrier, illustrated by solving a specific case.dividend policies, expected present value
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