Household decision-making with inflationary environment and the Cobb-Douglas utility

In this study, we investigate the optimal investment-consumption-insurance decisions faced by a wage earner operating within an inflationary environment, utilizing a continuous finite time framework. We posit that the wage earner’s preference is described by the Cobb-Douglas utility function, which incorporates a parameter that reflects the elasticity of substitution between consumption and leisure. Additionally, we assume that the financial market comprises three distinct financial assets: a risk-free bond, an index bond and a stock. To obtain closed-form solutions for optimal strategies and value function, we utilize the martingale method in conjunction with duality theory. Finally, the impact of several model parameters on optimal strategies is explored through numerical simulation utilizing predefined parameters.