Optimal surplus-dependent reinsurance under regime-switching in a Brownian risk model

Artikel

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.

Show object

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Risks ; ISSN: 2227-9091 ; Volume: 9 ; Year: 2021 ; Issue: 4 ; Pages: 1-25 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft
• Subject: boundary value problem ; Brownian motion ; HJB equation ; Markov chain ; optimal control ; ordinary differential equations ; regime-switching ; reinsurance

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Eisenberg, Julia ; Fabrykowski, Lukas ; Schmeck, Maren Diane
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2021

Further information

• DOI: doi:10.3390/risks9040073
• Handle: http://hdl.handle.net/10419/258161