Climbing the income ladder: Search and investment in a regime-switching affine income model

We study search and investment in an income ladder setting modeled by a regime-switching affine jump–diffusion income process with transition rates controlled by costly sequential search effort. The agent has exponential utility and can invest in a risky asset possibly correlated with the income process. Optimal policies are characterized explicitly, which allows us to identify the impact of risk aversion, search frictions, investment, and income risk in the agent's decisions. We illustrate our results with numerical examples. In particular, we find that search effort is reduced as the income mean-reversion increases or the hedging opportunities the financial markets offer increase.