Mutual aid insurance with a three-state Markov chain (Q6632361)

The authors of the paper describe a mathematical structure for mutual aid insurance through a three-state process, which is driven by an inhomogeneous Markov chain. They create a life-cycle stochastic control model to examine how mutual aid insurance influences an individual's life utility. The proposed model incorporates the three-state Markov chain to account for individual income stream fluctuations. In addition, the model allows the individual to make decisions about risky investments, consumption, and life insurance premiums. Using the corresponding Hamilton-Jacobi-Bellman equation, the authors obtain explicit expressions for optimal consumption, investment strategies, and life insurance premiums. The theoretical results of the paper are supplemented by numerical analysis