Explicit Solutions for Optimal Insurance Problems in Regime Switching Frameworks


  • Luca Di Persio University of Verona - Department of Computer Science
  • Samuele Vettori


Regime switching, insurance, stochastic optimization problem, Hamilton-Jacobi-Bellman equation, CRRA utility function, HARA utility function


The present paper treats the generalized Merton-type optimal consumption investmentproblem for a financial market whose characterizing parameters depend on the regime of theeconomy. In particular, we consider an agent which controls both his consumption and investment,as well as an insurance contract, and whose objective is to maximize the total discountedutility of consumption over an infinite horizon. In the case of Hyperbolic Absolute Risk Aversion(HARA) utility functions it is possible to obtain explicit solutions to the optimal consumption,investment and insurance problems, showing that the optimal strategies depend on the state of theeconomy. Exploiting latter result we perform a novel financial analysis assuming that the economyis characterized by three volatility regimes, also studying the impact of adding an exogenous wagein the investor’s wealth process.




How to Cite

Di Persio, L., & Vettori, S. (2014). Explicit Solutions for Optimal Insurance Problems in Regime Switching Frameworks. Asian Journal of Fuzzy and Applied Mathematics, 2(6). Retrieved from https://ajouronline.com/index.php/AJFAM/article/view/1974