Optimal Investment and Consumption Problem with Stochastic Environments

Optimal investment and consumption problem for a CRRA investor or agent is solved in this study. An invests the financial market with one risk-free security risky security. The stochastic interest rate dynamics of follow Ho-Lee model modeled as Heston’s its volatility parameter following Cox-Ingersoll-Ross (CIR) model. Interest rates rates, reality, are due to uncertain events such Coronavirus disease 2019 (COVID19) pandemic, climate change, etc. Our main goal allocate initial wealth x0 between order maximize discounted expected utility terminal over finite horizon. Applying Dynamic Programming Principle (DPP), HJB PDE value function established. power which belongs Constant Relative Risk Aversion (CRRA) class employed our analysis obtain optimal policies. Finally, numerical examples simulations provided discussed.