Created by Jan-Frederik Mai,Prof. Dr. Matthias Scherer

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 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.

Link to paper


Terms & Conditions
Please carefully read our Legal Notices and our Privacy Policy.

In this context, we must draw your particular attention to the following legal conditions:

Neither the information nor the opinions made available on this Website constitute an invitation, offer or recommendation to purchase, sell or otherwise dispose of a financial instruments, nor to make another transaction or to provide investment advice or any other service. Any investment decision relating to one of the products described herein must only be based on the respective sales documents (e.g. sales prospectus, semi-annual or annual reports, key investor information documents etc.).
The products referred to on this website may not be offered in all jurisdictions and may only be purchased by those investors entitled to do so. The information and contents of this website are not addressed to any persons or legal entities whose domicile prohibits the distribution of this information. All persons and legal entities whose domiciles are subject to a foreign jurisdiction should inform themselves about and observe these restrictions.

The information on this website is not addressed to the USA. US nationals, legal entities and persons with residence in the USA may not access this website. The information on this website may not be distributed or passed on in the USA. Xaia products referred to on this website will not be registered under the United States Securities Act of 1933 and no approval has been obtained in compliance with the US Commodities Exchange Act of 1936. Xaia products listed on this website may not be offered or sold in the USA either to citizens, or to US residents, or to legal entities domiciled in the USA.

The disclaimer confirmation of visitors to this website is stored as a necessary cookie on your device, is valid for a period of 90 days, however this can be reset at anytime by deleting your browser’s cookies.  For further information, please see our Privacy Policy.

Please provide your origin.
Please tell us whether you are an institutional or a private investor.
You have to agree, in order to use our online presence.