This talk presents results from the dissertations of the first two authors, supervised by the third. The common feature in both topics is the combination of simulation and optimization methods. Consider optimizing over variables x the expectation over other variables y of a function f(x,y), for high dimensional x and y. Here x is a portfolio allocation over mutual funds, y contains their future returns, and f is a future utility value, after encoding loads, taxes, and rebalancing. Complexity in f makes simulation natural. We handle it by using, and extending, a form of stochastic optimization. The second problem has to do with simulation based values for American options. There the hidden optimization is for an exercise policy. Instead of simply embedding this policy in a higher dimensional space, it makes more sense to work backwards from the final exercise date. We use simulations to extend a decision rule back one time step at a time, following Longstaff and Schwartz. We employ a flexible nonparametric rule (boosted decision trees) at each time step, and design the simulations taking account of the partially known simulation boundary.
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