# Case Study: Linear Regression in Tranche

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

PROBLEM 1: problem_lthranche_test
Minimize meansquare_err (Mean Squared Error)
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Dataset 5 10 79.60613 0.01 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

PROBLEM 2: problem_lthranche_style_classification
Minimize meanabs_pen(L1 Error)
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Dataset 5 1,264 0.0007085 0.02 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

CASE STUDY SUMMARY
An insurance company buys some protection from a reinsurance company. This case study solved a linear regression problem for building an optimal reinsurance contract (from the point of view of the insurance company buying reinsurance). The contract specifies loading coefficients for losses and attachment and detachment points of a tranche. The insurance company obtains reimbursement if the linear combination of the losses “hits” the tranche. The reimbursement equals the difference between the linear combination and the attachment point, under condition that the linear combination exceeds the attachment point. However the reimbursement does not exceed the width of the tranche (which is the difference between detachment and attachment points). The insurance company wants to match its losses projected to the tranche and reimbursements from the contract. In summary, the insurance company wants to find an optimal linear combination of losses in the contract specification to get a good protection in the specified tranche.