Abstract
In this paper, we solve two problems related to growth and survival probability maximization of an economy. We assume that the problems are subject to the stochastic net worth model introduced by Fleming and Stein (2004) and apply the techniques of stochastic optimal control theory in order to find our results. Via the results, we first establish the analytical specifications for the minimum goal reaching and maximum survival times of an economy. Given these, we show that the growth maximizing strategy enhances both the survival and goal reaching times besides its growth enhancing property. We also provide a closed form solution for the estimated debt crisis time of a non-resilient economy. Furthermore, by considering a fixed proportional consumption rate, we specify survival probability maximizing leverage as a function of this rate and show how optimal leverage strategy changes as the conditions of the economy changes. Mainly, we show that under bad economic conditions, bold leverage strategy must be followed at the expense of growth for the survival probability maximization. On the other hand, under good economic conditions, timid strategies are better as excessive risk taking must be avoided for the survival probability maximization. Again, for the same objective, we show that as an economy becomes less self sufficient, then, it needs to resort to external funds in order to finance its consumption, which may in turn lead excessive borrowing that may end up with debt crisis as it did in Greece.
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