JSM 2011 Online Program

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Abstract Details

Activity Number: 360
Type: Contributed
Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract - #302720
Title: Binary Prediction to Minimize Total Risk
Author(s): Kentaro Akashi and Yoshinori Kawasaki*+
Companies: Institute of Statistical Mathematics and Institute of Statistical Mathematics
Address: 10-3 Midori-cho, Tachikawa, Tokyo, International, 1908562, Japan
Keywords: binary prediction ; risk minimization ; optimal cutoff-point ; minimum prospective interval ; asymptotic theory
Abstract:

Risk involved with financial contracts often can be viewed as uncertainty of binary outcomes. This paper treat risk minimization as the problem of profit maximization, and gives an optimal solution of the cut-off point for binary prediction. This optimality or profit maximization will be asymptotically attained in the sense of convergence in probability. In practice, we have to replace the true parameters inside an indicator function by their estimates. Because indicator functions are discontinuous, apparently it looks non-standard argument. We show, in spite of this, that we can construct an interval for maximized profit, and even minimize it based on asymptotic theories where the MLE is simply plugged in. Simulation results suggest that the finite sample properties of our asymptotic theories are satisfactory. In an empirical analysis using personal loan data of a south German bank, we show the total profit realized by our optimal prediction exceeds the actually observed profit regardless of the settings of loan interest.


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