A Boundary Control Problem for a Nonlinear Parabolic by Maksimov V. I.

By Maksimov V. I.

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Extra resources for A Boundary Control Problem for a Nonlinear Parabolic Equation

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J This yields an LP model in standard form MaxJ =L L jeS keK j cjkYjk k L Y'k -13 L L P"Yjk = a. t. keK. J ieS keK. e. aj 0 and llij = 1. Note two features of this LP problem. First, the policies or strategies Yjk are randomized or mixed, since they combine the probabilities Zjk(t) over time. Second, a ~ stationary strategy is defined here by a function which for each state i one variable Yik where k E E S selects exactly K i . For stationary strategies it is easy to prove that if

He concluded that high rates of income growth and rapid structural change are positively correlated for those countries which are successful NICs. Here we propose entropy as a measure of structural change or structural diversification and argue that the optimal growth trajectory maximizes this entropy measure. This has two major implications. One is that the more successful a country is in terms of growth, the closer it will come towards the optimal trajectory associated with the maximum entropy.

1 k=1 q. log1t. ill This may characterize a risk averse optimal policy since it allows a fraction of the maximal average uncertainty in the objective function. Next we consider another application of the transition probability model to the investment allocation for different mutual funds analyzed in some detail by Dumas and Sengupta (1991). It is well known that an investor can reduce the risk of investment by allocating wealth to a variety of assets. Hence mutual funds provide an attractive form of investment for those individuals who do not possess enough wealth to construct a diversified portfolio.

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