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Log-optimal investment
Král, Stanislav ; Dostál, Petr (advisor) ; Večeř, Jan (referee)
1. Abstrakt Suppose we have a capital, which we will redistribute into investment op- portunities. The financial valuation of these investments will be a sequence of independent, identically distributed random vectors that acquire finite amount of values. We will have full knowledge of the entire history of these valuations before each investment. It turns out that if our strategy is to always maximizes the mean value of the logarithm of the investment value, denoted by Λ∗ , then this strategy is asymptotically the best one possible. If strategy Λ is not asymptotically close to Λ∗ and if x goes to infinity, then the mean of the time we earn atleast x using Λ∗ is infinitely smaller than the time if we used Λ. We also earn infinitely times more money using the strategy Λ∗ . 1
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Kelly criterion in portfolio selection problems
Dorová, Bianka ; Kopa, Miloš (advisor) ; Omelka, Marek (referee)
In the present work we study portfolio optimization problems. Introduction is followed by chapter 2, where we introduce the concept of utility function and its relationship to the investor's risk attitude. To solve the optimization problem we consider the Markowitz portfolio optimization model and the Kelly criterion, which are recalled in the fourth and fifth chapter. The work also contains an extensive numerical study. Using the optimization software GAMS we solve portfolio optimization problems. We consider a portfolio problem with (and without) allowed short sales. We compare the obtained portfolios and we discuss whether Kelly optimal portfolio is a special case of the Markowitz optimal portfolio for the special value of the minimum expected return.
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Log-optimal investment
Král, Stanislav ; Dostál, Petr (advisor) ; Večeř, Jan (referee)
Suppose we have capital, which we will redistribute into investment oppor- tunities. The financial valuation of these investments will form a sequence of independent, identically distributed random vectors taking values in some clo- sed, positive interval. We will have full knowledge of the entire history of these valuations before each investment. It turns out that if our strategy is to always maximize the mean value of the logarithm return on these investments, then this strategy is in a sense asymptotically optimal. 1
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Log-optimal investment
Král, Stanislav ; Dostál, Petr (advisor) ; Večeř, Jan (referee)
1. Abstrakt Suppose we have a capital, which we will redistribute into investment op- portunities. The financial valuation of these investments will be a sequence of independent, identically distributed random vectors that acquire finite amount of values. We will have full knowledge of the entire history of these valuations before each investment. It turns out that if our strategy is to always maximizes the mean value of the logarithm of the investment value, denoted by Λ∗ , then this strategy is asymptotically the best one possible. If strategy Λ is not asymptotically close to Λ∗ and if x goes to infinity, then the mean of the time we earn atleast x using Λ∗ is infinitely smaller than the time if we used Λ. We also earn infinitely times more money using the strategy Λ∗ . 1
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Kelly criterion in portfolio selection problems
Dorová, Bianka ; Kopa, Miloš (advisor) ; Omelka, Marek (referee)
In the present work we study portfolio optimization problems. Introduction is followed by chapter 2, where we introduce the concept of utility function and its relationship to the investor's risk attitude. To solve the optimization problem we consider the Markowitz portfolio optimization model and the Kelly criterion, which are recalled in the fourth and fifth chapter. The work also contains an extensive numerical study. Using the optimization software GAMS we solve portfolio optimization problems. We consider a portfolio problem with (and without) allowed short sales. We compare the obtained portfolios and we discuss whether Kelly optimal portfolio is a special case of the Markowitz optimal portfolio for the special value of the minimum expected return.
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