4. Conclusion

There are some financial optimal control models where the given fitting functions are cos or sin functions; then the financial control needs to take three values with the middle being zero, to ensure a good approximation. The experiment in Section 5.3.1 verifies the accuracy of the algorithms 3.1-3.4, thus the computer software package CSTVA (for details see Appendix A.4) based on these algorithms can solve all these kinds of control problems. The computed results provide insights into the dynamics of the financial system in terms of the state and control variables.

This page intentionally left blank

Chapter 6

CONCLUSION

Modeling and computation of dynamic optimization problems in finance is an important area for research in financial modeling. The thrust of this research has been to develop computational methods in order to solve financial optimal control models which are difficult to solve by traditional analysis using optimal control theories. Four computer software packages called CSTVA have been constructed, each of them used for different optimal control problems in two areas of finance: optimal investment planning and optimal corporate financing.

The STV approach consists of the following six major computational methods:

1 An optimization program based on the sequential quadratic programming (SQP)

2 The switching time variable method, the switching time is made a control variable.

3 The finite difference method for estimating gradients when gradients are not provided.

4 The step function approach to approximate the control variable.

5 A piecewise-linear (or non linear) transformation of time (as in MATLABs constr program similar to the Newton Method for constrained optimization).

6 Second order differential equations represent the oscillatory dynamic financial models.