By Chen P., Islam S.M.N.
The choice of optimum financing and funding recommendations (optimal capital constitution or optimum mixture of money, optimum portfolio selection, etc.) for companies and the financial system are very important for effective allocation of assets within the financial system. optimum keep watch over equipment have worthy purposes to those parts in finance - a few optimization difficulties in finance comprise optimum keep watch over, related to a dynamic process with switching instances within the kind of bang-bang keep an eye on. optimum keep an eye on types for company finance and the economic system are offered during this publication and the analytical and computational result of those versions also are mentioned. Such computational techniques to the examine of optimum company financing aren't renowned within the latest literature. This e-book develops a brand new computational technique the place switching instances are regarded as variables within the optimum dynamic monetary version represented through a moment order differential equation. a brand new desktop software named CSTVA (Computer software for the Switching Time Variables Algorithm), which could compute bang-bang optimum monetary versions with switching time, can be built. optimum financing implications of the version ends up in the shape of optimum switching occasions for alterations in financing rules and the optimum monetary regulations are analyzed.
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Extra info for Optimal Control Models in Finance: A New Computational Approach
In turn, “constr” calls the “Minimization Program” to calculate the minimization of the calling program with respect to the optimal vector um. Step 3. Input the optimal result um into “Minimization Program”, to obtain the values of the objective function J(nn) (the last value of the integral) and state vector xm (xm is a vector of all the values of the state functions take at the grid-points of the switching time intervals). Step 4. Attach a cost K to nn. 2) and calculate Step 5. Set a bigger nn and new starting time intervals, go back to Step 2; EXIT when the result of cost function J stops decreasing.
7, different numbers of switching times lead to different results for the objective function of the financial model. While the number of switching times increases, the value of the objective function decreases. That means a better fit is obtained. When a cost of changing control at each switching time is added to the original objective, the perspective changes. In the present case, when the number of switching times increases, the value of the term, which includes cost and the number of the switching, also increases.
Approaches to Bang-Bang Optimal Control with a Cost of Changing Control In this section, the computational methods for solving bang-bang optimal control problems with a cost of switching control are introduced. Simply modifying certain parts of these methods can satisfy a class of similar problems. 7) as a function of the switching times, say Then the minimum of this function is computed, starting from a small value of N. Here the components of the vector are the lengths between each switching time.