Optimal switching between two spectrally negative Lévy processes to minimise ruin probability

Loeffen, Ronnie and Martínez Sosa, José Eduardo and Van Schaik, Kees (2020) Optimal switching between two spectrally negative Lévy processes to minimise ruin probability. [MIMS Preprint]

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Abstract

We consider an optimal underwriting problem where given two insurance portfolios that generate cash flows according to two spectrally negative Lévy processes of bounded variation X and Y, one has to underwrite adaptively a convex combination of the two such that the probability of ruin occurring in the combined portfolio is minimised. This optimal underwriting problem boils down to an optimal switching problem where one has to decide, based on the available capital at a given time, whether to go for mode $X$ or for mode $Y$ at that time. The 1-switch-level strategy with parameter b in [0,oo] is the strategy where one switches from one mode to the other only at times when the capital goes above or below the level b. We find a set of sufficient conditions on the two Lévy measures such that an optimal strategy is formed by a 1-switch-level strategy, which covers in particular the case where the hazard rates of the two Lévy measures are decreasing and ordered. An interesting tool in the analysis is a new monotonicity property regarding quasi-convexity for renewal equations.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Dr Ronnie Loeffen
Date Deposited: 27 Aug 2020 09:15
Last Modified: 27 Aug 2020 09:15
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2779

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