Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258161 
Year of Publication: 
2021
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 9 [Issue:] 4 [Article No.:] 73 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-25
Publisher: 
MDPI, Basel
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.
Subjects: 
boundary value problem
Brownian motion
HJB equation
Markov chain
optimal control
ordinary differential equations
regime-switching
reinsurance
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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