Abstract
The paper presents a model that combines a dynamic programming (stochastic optimal control) approach and a multi-stage stochastic linear programming approach (SLP), integrated into one SLP
formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement. However, explicit solution may not exist, especially when we want to deal with constraints, such as the limits on the portfolio composition, the limits on the insured sum, an inclusion of transaction costs or taxes on capital gains, which are important issues regularly mentioned in the scientic literature. Two applications are considered: (A) optimal investment, consumption and insured sum for an individual maximizing the expected utility of consumption and bequest, and (B) optimal investment for a pension saver who wishes to maximize the expected utility of retirement benets. Numerical results show that among the considered practical constraints, the presence of taxes aects the optimal controls the most. Furthermore, the individual's preferences, such as impatience level and risk aversion, have even a higher impact on the controlled processes than the taxes on capital gains.
formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement. However, explicit solution may not exist, especially when we want to deal with constraints, such as the limits on the portfolio composition, the limits on the insured sum, an inclusion of transaction costs or taxes on capital gains, which are important issues regularly mentioned in the scientic literature. Two applications are considered: (A) optimal investment, consumption and insured sum for an individual maximizing the expected utility of consumption and bequest, and (B) optimal investment for a pension saver who wishes to maximize the expected utility of retirement benets. Numerical results show that among the considered practical constraints, the presence of taxes aects the optimal controls the most. Furthermore, the individual's preferences, such as impatience level and risk aversion, have even a higher impact on the controlled processes than the taxes on capital gains.
| Original language | English |
|---|---|
| Journal | OR Spectrum - Quantitative Approaches in Management |
| Volume | 37 |
| Issue number | 3 |
| Pages (from-to) | 583-616 |
| ISSN | 0171-6468 |
| DOIs | |
| Publication status | Published - 2015 |
Keywords
- Dynamic programming
- Multi-period stochastic linear programming
- Power utility
- Personal finance, retirement