Volume 56, Number 5, September-October 2022
|Page(s)||3611 - 3634|
|Published online||19 October 2022|
Optimal investment and reinsurance on survival and growth problems for the risk model with common shock dependence
Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
2 School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 16 September 2022
This paper investigates goal-reaching problems regarding optimal investment and proportional reinsurance with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. The optimization problems are formulated in a general form first, and then four criteria including maximum survival probability, minimum expected ruin penalty, minimum (maximum) expected time (reward) to reach a goal are fully discussed. By the technique of stochastic control theory and through the corresponding Hamilton–Jacobi–Bellman equation, the optimal results are derived and analyzed in different cases. In particular, when discussing the maximum survival probability with a target level U beyond the safe level (where ruin can be avoided with certainty once it is achieved), we construct ε-optimal (suboptimal) strategies to resolve the inaccessibility of the safe level caused by classical optimal strategies. Furthermore, numerical simulations and analysis are presented to illustrate the influence of typical parameters on the main results.
Mathematics Subject Classification: 60J60 / 62P05 / 91B28 / 91B30 / 93E20
Key words: Proportional reinsurance / common shock dependence / stochastic control / ε-optimal (suboptimal) strategy / Hamilton–Jacobi–Bellman equation
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.