An explicit linear solution for the quadratic dynamic programming problem

1988 ◽  
Vol 58 (2) ◽  
pp. 319-330 ◽  
Author(s):  
W. R. S. Sutherland ◽  
H. Wolkowicz ◽  
V. Zeidan
Author(s):  
Sergey Ivanovich Makarov ◽  
◽  
Maria Vladimirovna Kurganova ◽  

The dynamic programming problem for finding the optimal operating period and equipment replacement time using a combination of graphical and calculation methods of economic analysis is considered.


2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenjie Bi ◽  
Liuqing Tian ◽  
Haiying Liu ◽  
Xiaohong Chen

Dynamic portfolio choice is an important problem in finance, but the optimal strategy analysis is difficult when considering multiple stochastic volatility variables such as the stock price, interest rate, and income. Besides, recent research in experimental economics indicates that the agent shows limited attention, considering only the variables with high fluctuations but ignoring those with small ones. By extending the sparse max method, we propose an approach to solve dynamic programming problem with small stochastic volatility and the agent’s bounded rationality. This approach considers the agent’s behavioral factors and avoids effectively the “Curse of Dimensionality” in a dynamic programming problem with more than a few state variables. We then apply it to Merton dynamic portfolio choice model with stochastic volatility and get a tractable solution. Finally, the numerical analysis shows that the bounded rational agent may pay no attention to the varying equity premium and interest rate with small variance.


1977 ◽  
Vol 12 (4) ◽  
pp. 629-629
Author(s):  
William R. Folks

This paper extends the results of previous work by the author in the development of a structure for analysis of rather general two-currency decision problems using an nstage dynamic programming model. After a brief review of the model, the paper provides a characterization of a convertibility scheme as a set function which assigns to each currency portfolio a set of currency portfolios which can be attained from the original portfolio, operating through the convertibility scheme. The concept of a substitutable convertibility scheme is developed; the substitutability property allows the decision maker to substitute a functionally determined single currecy payoff for a given twocurrency payoff. Two tests to determine substitutability in general, and for a particular return function, are developed. The modest reduction in dimensionality of the dynamic programming problem arising from this property is explained. Some specific convertibility schemes are then characterized, including free convertibility, inconvertibility, retention quotas, maximum balance, maximum acquisition, and multiple rate schemes. The substitutability of free convertibility is demonstrated. A retention quota scheme which allows free sale and purchase of retained funds in a parallel market is shown to be equivalent to a free convertibility scheme, and therefore substitutable.


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