Ruin models with investment income. (English) Zbl 1189.91077

Summary: 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 [J. Paulsen, Insur. Math. Econ. 22, No. 1, 3–16 (1998; Zbl 0909.90115)].


91B30 Risk theory, insurance (MSC2010)
91G80 Financial applications of other theories
60G44 Martingales with continuous parameter
60G40 Stopping times; optimal stopping problems; gambling theory
60K05 Renewal theory
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance


Zbl 0909.90115
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