Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model

Julia Eisenberg, Lukas Fabrykowski and Maren Diane Schmeck
Additional contact information
Julia Eisenberg: Department of Financial and Actuarial Mathematics, TU Wien, Wiedner Hauptstraße 8–10/E105-1, 1040 Vienna, Austria
Lukas Fabrykowski: Triangular IT Solutions e.U., 1220 Vienna, Austria
Maren Diane Schmeck: Center for Mathematical Economics, Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany

Risks, 2021, vol. 9, issue 4, 1-25

Abstract: In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company’s surplus process is assumed to follow a Brownian motion with drift, and the reinsurance price is modelled by a continuous-time Markov chain with two states. The presence of regime-switching substantially complicates the optimal reinsurance problem, as the surplus-independent strategies turn out to be suboptimal. We develop a recursive approach that allows to represent a solution to the corresponding Hamilton–Jacobi–Bellman (HJB) equation and the corresponding reinsurance strategy as the unique limits of the sequence of solutions to ordinary differential equations and their first- and second-order derivatives. Via Ito’s formula, we prove the constructed function to be the value function. Two examples illustrate the recursive procedure along with a numerical approach yielding the direct solution to the HJB equation.

Keywords: reinsurance; regime-switching; Brownian motion; Markov chain; optimal control; HJB equation; ordinary differential equations; boundary value problem (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-9091/9/4/73/pdf (application/pdf)
https://www.mdpi.com/2227-9091/9/4/73/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:9:y:2021:i:4:p:73-:d:535490

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().