Portfolio Optimization for Credit-Risky Assets under Marshall–Olkin Dependence

A stochastic gradient descent algorithm to maximize power utility of large credit portfolios under Marshall–Olkin dependence

“…While being simple in a theoretical sense, unfortunately the Marshall-Olkin distribution suffers from the curse of dimensionality for moderate to large asset universes, so that it is not as simple as the multivariate normal distribution from a practical perspective, i.e. the implementation is not solved satisfactorily in [19]. The present article fills this gap.…”

“…Having the Markowitz/Merton paradigm in mind, we thus consider it natural to replace the multivariate normal distribution as reasonable basis for an equity-return model with the simplest reasonable multivariate exponential distribution as basis for a portfolio credit-risk model. In our view, there are striking arguments in favor of the Marshall-Olkin multivariate exponential distribution [24] to claim this role as being the most natural generalization of the exponential law in higher dimensions and thus serving as model for the default times, see [19,Section 2] and the main body of the present article. This opinion follows the arguments of [17,10,8,5,33], all applying the Marshall-Olkin distribution in credit-risk modeling because of its appealing trade-off between tractability and realism.…”

“…The consequence of altering the distributional assumption in the aforementioned optimality justification result by R.C. Merton [26,27] is a technical one; but conceptually the philosophy of optimizing an expected utility can still be used, accomplished in 2 [19], which is an application of 3 [28]. While being simple in a theoretical sense, unfortunately the Marshall-Olkin distribution suffers from the curse of dimensionality for moderate to large asset universes, so that it is not as simple as the multivariate normal distribution from a practical perspective, i.e.…”

“…They do, however, typically fall short of being ready to use in practical applications; especially for large investment universes. Well-known papers in this strand of literature are, e.g., [6,7,15,16,19]. In contrast, we aim at providing the first model for credit-portfolio selection that satisfies all of the aforementioned desiderata and can thus be accepted by both the theoretical and practical community.…”

“…In contrast, we aim at providing the first model for credit-portfolio selection that satisfies all of the aforementioned desiderata and can thus be accepted by both the theoretical and practical community. To achieve this, we resort to the model introduced and theoretically justified in [19], which to date, however, is not ready for real-world applications. Observing that both the practical parameter design and the numerical implementation is still not straightforward, thus unsolved in [19], we put emphasis on exactly these challenges and provide concrete advice in order to prepare the model for practical use.…”