Jan-Frederik Mai,Prof. Dr. Matthias Scherer
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 with arbitrarily many assets. 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.
Static pricing-hedging duality for credit default swaps and the negative basis arbitrage
Portfolio selection based on graphs: does Mr. Markowitz have his finger in the pie?