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

A vector of bankruptcy times with Marshall–Olkin multivariate exponential distribution implies a simple, yet reasonable, continuous-time dynamic model for dependent credit-risky assets with an appealing trade-off between tractability and realism. Within this framework the maximization of expected power utility of terminal wealth requires the maximization of a concave function on a polygon, a numerical problem whose complexity grows exponentially in the number of considered assets. We demonstrate how to solve this seemingly impractical numerical problem reliably and efficiently in order to prepare the model for practical use cases. To this end, we resort to a specifically designed factor construction for the Marshall–Olkin distribution that separates dependence parameters from idiosyncratic parameters, and we develop a tailor-made stochastic gradient descent algorithm with random constraint projections for the model’s numerical implementation.     «

A vector of bankruptcy times with Marshall–Olkin multivariate exponential distribution implies a simple, yet reasonable, continuous-time dynamic model for dependent credit-risky assets with an appealing trade-off between tractability and realism. Within this framework the maximization of expected power utility of terminal wealth requires the maximization of a concave function on a polygon, a numerical problem whose complexity grows exponentially in the number of considered assets. We demonstrat...     »