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Application of outer approximation to forecasting losses and scenarios in the target of portfolios with high of nonlinear risk

Katsuhiro Tanaka (pwd5re227i***at***hotmail.co.jp)

Abstract: The purpose of this paper is to find appropriate solutions to concave quadratic programming using outer approximation algorithm, which is one of the algorithm of global optimization, in the target of the strong of concavity of object function i.e. high of nonlinear risk of portfolio. Firstly, my target model is a mathematical optimization programming to forecast scenarios and losses in the case of realistic interest rate portfolio. Object function of the model is quadratic function for representing portfolio loss using delta, gamma and vega. And, it becomes concave quadratic programming i.e. nonlinear programming, and is not guaranteed to find appropriate solution in using some general solver. However, it is possible to find appropriate solution in using a specific outer approximation algorithm. Secondly, my target case is in the high of nonlinear risk of portfolio, because main business of financial institution is to sell various financial product such as options, and then they are obliged to have highly nonlinear risk. Major nonlinear risk is vega, which tend to be negative in selling options. And negative of vega make quadratic function concave, because diagonal component of quadratic coefficient matrix become negative. Therefore, my target case is in the strong of concavity of object function. Lastly, I check that there exists relationship of negative correlation between high of nonlinear risk i.e. strong of concavity of quadratic function and calculation cost. Therefore, when it apples outer approximation algorithm to my target model and case, I see that it is very useful from the perspective of computation as well as risk management. I believe that this paper will be of interest to researchers and practitioners in the field of market risk management in the financial industry.

Keywords: Risk management, Mathematical optimization, Outer approximation, Concave quadratic objective function, Forecasting of scenario and loss

Category 1: Applications -- OR and Management Sciences (Finance and Economics )

Category 2: Global Optimization (Applications )


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Entry Submitted: 01/15/2019
Entry Accepted: 01/15/2019
Entry Last Modified: 01/15/2019

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