The starting point of this master thesis is the portfolio optimization framework for credit risky assets under Marshall-Olkin dependence developed in [1]. The optimal portfolio allocation in this model leads to an optimization problem that requires the evaluation of a function, which becomes numerically burdensome for a large asset universe. To overcome this diffculty, we find an unbiased estimator of the function's gradient, which we refer to as a stochastic gradient. This suggests that we could tackle the optimization problem using a stochastic gradient algorithm. To develop a mechanism that generates realizations of the random gradient, we exploit the Lévy subordinator construction of the Marshall-Olkin distribution from [2], [3]. We study the properties of the objective function with the aim to use already established results on the convergence of the stochastic gradient algorithm. Finally, based on these results, we compute the optimal portfolio for a special subclass of the Marshall-Olkin distribution and observe the performance of the algorithm for different number of assets.     «

The starting point of this master thesis is the portfolio optimization framework for credit risky assets under Marshall-Olkin dependence developed in [1]. The optimal portfolio allocation in this model leads to an optimization problem that requires the evaluation of a function, which becomes numerically burdensome for a large asset universe. To overcome this diffculty, we find an unbiased estimator of the function's gradient, which we refer to as a stochastic gradient. This suggests that we coul...     »