Optimal social welfare policy within financial and life insurance markets

Abstract

We consider a continuous lifetime model for investor whose lifetime is a random variable. We assume the investor has an access to the social welfare system, the financial market and the life insurance market. The investor aims to find the optimal strategies that maximize the expected utility obtained from consumption, investing in the financial market, buying life insurance, registering in the social welfare system, the size of his estate in the event of premature death and the size of his fortune at time of retirement if he lives that long. We use dynamic programming techniques to derive a second-order nonlinear partial differential equation whose solution is the maximum objective function. We use special case of discounted constant relative risk aversion utilities to find an explicit solutions for the optimal strategies. Finally, we have shown a numerical solution for the problem under consideration and study some properties for the optimal strategies.

Keywords:

• Optimal consumption
• optimal investment
• optimal life insurance selection
• optimal social welfare policy
• stochastic optimal control
• dynamic programming
• Hamilton–Jacobi–Bellman equation

2000 Mathematics Subject Classifications:

• 49J20
• 93E20
• 60H10

Acknowledgements

We thank the three anonymous reviewers whose useful comments and suggestions helped to improve and clarify this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Abdelrahim S. Mousa and Moath Hoshiea thank Birzeit University for the financial support through the project 33/2021. A. A. Pinto thanks the financial support of LIAAD-INESC TEC and FCT-Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within the project Modelling, Dynamics and Games, with reference PTDC/MAT-APL/31753/2017.