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The distribution of refracted Lévy processes with jumps having rational Laplace transforms

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  30 November 2017

Jiang Zhou  and
Lan Wu
Jiang Zhou*
Affiliation:
Peking University
Lan Wu*
Affiliation:
Peking University
*
* Postal address: School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China.
* Postal address: School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China.
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Abstract

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulae for the Laplace transform of its distribution. Our formulae are presented in an attractive form and the approach is novel. In particular, the idea in the application of an approximating procedure is remarkable. In addition, the results are used to price variable annuities with state-dependent fees.

Keywords

Refracted Lévy processrational Laplace transformcontinuity theoremWiener–Hopf factorizationvariable annuitystate-dependent fee

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 91B30: Risk theory, insurance
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 1167 - 1192
Copyright
Copyright © Applied Probability Trust 2017 

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