Classical solutions of the backward PIDE for Markov modulated marked point processes and applications to CAT bonds

Katia Colaneri and Rüdiger Frey

Insurance: Mathematics and Economics, 2021, vol. 101, issue PB, 498-507

Abstract: The objective of this paper is to give conditions ensuring that the backward partial integro differential equation associated with a multidimensional jump-diffusion with a pure jump component has a unique classical solution; that is the solution is continuous, twice differentiable in the diffusion component and differentiable in time. Our proof uses a probabilistic argument and extends the results of Pham (1998) to processes with a pure jump component where the jump intensity is modulated by a diffusion process. This result is particularly useful in some applications to pricing and hedging of financial and actuarial instruments, and we provide an example to pricing of CAT bonds.

Keywords: Partial integro differential equations; Classical solution; Markov modulated marked point process; Cauchy problem; CAT bonds (search for similar items in EconPapers)
JEL-codes: C02 C61 G12 G22 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:101:y:2021:i:pb:p:498-507

DOI: 10.1016/j.insmatheco.2021.09.003

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