Consumption, investment and life insurance under different tax regimes

We study the effects of introducing taxation in classical continuous-time optimization problems with utility from consumption, bequest and retirement savings. Inspired by actual tax favoured retirement savings programs, we formulate and solve the optimization problem for various tax regimes, and compare tax effects on consumption/savings contributions, investment and purchase of life insurance under the regimes. The optimization problems have analytical solutions, which allow for easy comparison of tax effects under the different regimes. To substantiate the results we also present a numerical analysis of the results based on realistic parameter values and regimes. Based on American and Danish tax regimes we estimate the values of existing retirement saving favouring to be 1-2 percent of lifetime income.