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Ruin theory with stochastic return on investments

Part of: Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Jostein Paulsen  and
Håkon K. Gjessing
Jostein Paulsen*
Affiliation:
University of Bergen
Håkon K. Gjessing*
Affiliation:
Haukeland Hospital
*
*Postal address: Department of Mathematics, University of Bergen, 5008 Bergen, Norway.
**Postal address: Division for Medical Statistics, AHH, Haukeland Hospital, 5021 Bergen, Norway.
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Abstract

We consider a risk process with stochastic interest rate, and show that the probability of eventual ruin and the Laplace transform of the time of ruin can be found by solving certain boundary value problems involving integro-differential equations. These equations are then solved for a number of special cases. We also show that a sequence of such processes converges weakly towards a diffusion process, and analyze the above-mentioned ruin quantities for the limit process in some detail.

Keywords

RUIN THEORYSTOCHASTIC DIFFERENTIAL EQUATIONINTEGRO-DIFFERENTIAL EQUATIONWEAK CONVERGENCE

MSC classification

Secondary: 60H10: Stochastic ordinary differential equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 4 , December 1997 , pp. 965 - 985
Copyright
Copyright © Probability Trust 1997 

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