Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

Keywords: Personal finance, multi-state model, stochastic control, financial decision making, mortality-disability-unemployment risk.