By Robert Dochow

Robert Dochow mathematically derives a simplified category constitution of chosen varieties of the portfolio choice challenge. He proposes new aggressive on-line algorithms with danger administration, which he evaluates analytically. the writer empirically evaluates on-line algorithms via a entire statistical research. Concrete effects are that follow-the-loser algorithms convey the main promising functionality while the target is the maximization of go back on funding and risk-adjusted functionality. additionally, while the target is the minimization of danger, the 2 new algorithms with probability administration express very good functionality. A prototype of a software program instrument for computerized overview of algorithms for portfolio choice is given.

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At the time instant when the investor is not allowed to trade, it is not possible to reallocate the asset proportions such that the portfolio is rebalanced to the specific target allocation. The problem is described by Kozat and Singer [2011] and defined as semi-constant rebalancing problem (SCRP). More formal: Trading is not executed in some time instants such that bit , the proportion for Ai at time instant (t − 1), is not reallocated to a specific target proportion. , m can not be true. 3 allocation is not possible.

2. It can be seen that the investor holds only one asset for the full investment horizon. This is the one with the largest value for qqiT with i = 1, 2, which is the best asset in the market during i0 34 2 Portfolio Selection Problems the investment horizon. Obviously, the search for the best buy-and-hold portfolio when maximizing terminal wealth is always equal to the search for the best asset. Note that the best buy-and-hold portfolio (BH) contains only one asset if the objective is to maximize terminal wealth, such that bit ∈ {0, 1}.

2 Portfolio Selection Problems The portfolio selection problem exists in a variety of forms. In this chapter the main types of the portfolio selection problem from the literature are classified and presented as mathematical programs. The types are introduced from the perspective of an investor who buys and sells shares of assets at time instants. To derive a classification structure among the considered types of the portfolio selection problem all of them are simplified in two ways. First, each type of problem aims to maximize the wealth of the investor at the end of the investment horizon.

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