An Elementary Introduction to Dynamic Programming: A State Equation Approach"When the Japanese landed at Rabaul on Friday 23 January 1942 it was the start of one of the fiercest campaigns of the war. On that day, with only a handful of badly trained troops led by inexperienced officers, with a civil administration torn with incompetence and jealousies, Australia faced its most serious threat yet. For Australia itself was one of the most important targets"--Jacket. |
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Page 40
... intuitively reasonable . Here we use manipulations that are mathemati- cally rigorous . As we have stated previously ... intuition will deepen our insight into the methods we subsequently use . Let us first define the problems P2 ( x1 ) ...
... intuitively reasonable . Here we use manipulations that are mathemati- cally rigorous . As we have stated previously ... intuition will deepen our insight into the methods we subsequently use . Let us first define the problems P2 ( x1 ) ...
Page 173
... intuition failed us , since the optimal policy is not always to bet as little as possible in this losing game , as we ... intuitively reasonable results that are indeed true . First , that f ( x ) decreases monotoni- cally with r , as is ...
... intuition failed us , since the optimal policy is not always to bet as little as possible in this losing game , as we ... intuitively reasonable results that are indeed true . First , that f ( x ) decreases monotoni- cally with r , as is ...
Page 195
... intuition . Note also that we are re- quiring more information than he does , or thinks he does : we require an estimate of the variance of the random fluctuations about the trend . In a sense , investors are intuitively very much aware ...
... intuition . Note also that we are re- quiring more information than he does , or thinks he does : we require an estimate of the variance of the random fluctuations about the trend . In a sense , investors are intuitively very much aware ...
Contents
Introduction | 1 |
An InvestmentAllocation Problem | 6 |
A Simple Dynamic Optimization Problem and Its Relationship | 23 |
Copyright | |
14 other sections not shown
Common terms and phrases
analogously to Eq analytical assume Bayesian Bayesian probabilities boundary C₁ chapter choose computationally computer storage consider constant stock level corresponding decisions v₁ defined determine deterministic dimensionality discrete search discussion dynamic programming example fi(x final finite fo(x functional equations g(xo gambler's ruin gives grid H₁ H₂ increases induction infinite-stage process initial state xo integer inventory Lagrange multipliers mathematical Max h(x Max v² maximize methods minimize module monotonically multi-stage decision processes N-stage process notation Note obtain optimal decisions optimal policy p₁ parameters particle path criterion function possible principle of optimality probability problem process starting random variable random walk reader respectively result right-hand side sequential sequential analysis Similarly simulation solve stage stochastic stochastic processes sub-optimal successive approximations Suppose tables tions v₁² v₂ v₂² values variable Vs+1 vz² x-range x₁ Xs+1 zero