## In this dissertation, the solution of portfolio optimization by maximizing expected utility of wealth function subjected to income tax and capital gains tax is found. In this investment problem, an investor has two assets namely risk free asset (e.g bond) and risky asset (e.g stocks). The evolution of the risk free asset is described deterministically while the dynamics of the risky asset is described by the geometric mean reversion (GMR) model which incorporate dividend and income tax. The portfolio optimization problem is then successfully formulated and solved with DPP and HJB equations. The results showed that the optimal investment strategy is dependent on wealth and income tax. The optimal investment strategy is not affected by capital gains tax, because capital gains tax come into effect at redemption and our investor holds his portfolio before redemption. In this dissertation, power, exponential and logarithmic utility functions are considered. It is found that, when power and logarithmic utility functions are used, an investor exhibits constant relative risk aversion but optimal investment strat- egy decreases as the wealth increases. In case of exponential utility function an investor exhibits increasing relative risk aversion and the optimal investment strategy decreases as the wealth increases. Finally, in all three cases of utility function, if the investor increases his proportion of wealth in the risky assets then income tax is also increases.

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##### Date

2013

##### Authors

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##### Volume Title

##### Publisher

University of Dar es Salaam

##### Abstract

In this dissertation, the solution of portfolio optimization by maximizing expected utility of wealth function subjected to income tax and capital gains tax is found. In this investment problem, an investor has two assets namely risk free asset (e.g bond) and risky asset (e.g stocks). The evolution of the risk free asset is described deterministically while the dynamics of the risky asset is described by the geometric mean reversion (GMR) model which incorporate dividend and income tax. The portfolio optimization problem is then successfully formulated and solved with DPP and HJB equations. The results showed that the optimal investment strategy is dependent on wealth and income tax. The optimal investment strategy is not affected by capital gains tax, because capital gains tax come into effect at redemption and our investor holds his portfolio before redemption. In this dissertation, power, exponential and logarithmic utility functions are considered. It is found that, when power and logarithmic utility functions are used, an investor exhibits constant relative risk aversion but optimal investment strat-
egy decreases as the wealth increases. In case of exponential utility function an investor exhibits increasing relative risk aversion and the optimal investment strategy decreases as the wealth increases. Finally, in all three cases of utility function, if the investor increases his proportion of wealth in the risky assets then income tax is also increases.

##### Description

Available in print form, EAF collection, Dr. Wilbert Chagula Library, class mark ( THS EAF 4529.2.M854 )

##### Keywords

Investiments, Optimal investiment, Income tax, Capital gain tax, Matematical models

##### Citation

Mwigilwa, W ( 2013 ) In this dissertation, the solution of portfolio optimization by maximizing expected utility of wealth function subjected to income tax and capital gains tax is found. In this investment problem, an investor has two assets namely risk free asset (e.g bond) and risky asset (e.g stocks). The evolution of the risk free asset is described deterministically while the dynamics of the risky asset is described by the geometric mean reversion (GMR) model which incorporate dividend and income tax. The portfolio optimization problem is then successfully formulated and solved with DPP and HJB equations. The results showed that the optimal investment strategy is dependent on wealth and income tax. The optimal investment strategy is not affected by capital gains tax, because capital gains tax come into effect at redemption and our investor holds his portfolio before redemption. In this dissertation, power, exponential and logarithmic utility functions are considered. It is found that, when power and logarithmic utility functions are used, an investor exhibits constant relative risk aversion but optimal investment strat- egy decreases as the wealth increases. In case of exponential utility function an investor exhibits increasing relative risk aversion and the optimal investment strategy decreases as the wealth increases. Finally, in all three cases of utility function, if the investor increases his proportion of wealth in the risky assets then income tax is also increases, Masters dissertation, University of Dar es Salaam, Dar es Salaam