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Mortgage loan portfolio optimization using multi-stage stochastic programming. (English) Zbl 1163.91420
Summary: We consider the dynamics of the Danish mortgage loan system and propose several models to reflect the choices of a mortgagor as well as his attitude towards risk. The models are formulated as multi-stage stochastic integer programs, which are difficult to solve for more than 10 stages. Scenario reduction [see J. Dupačova, N. Growe-Kuska and W. Römisch, Math. Program. 95, No. 3(A), 493–511 (2003; Zbl 1023.90043), H. Heitsch and W. Römisch, Comput. Optim. Appl. 24, No. 2–3, 187–206 (2003; Zbl 1094.90024)] and LP relaxation are used to obtain near optimal solutions for large problem instances. Our results show that the standard Danish mortgagor should hold a more diversified portfolio of mortgage loans, and that he should rebalance the portfolio more frequently than current practice.

91G10 Portfolio theory
90C90 Applications of mathematical programming
90C15 Stochastic programming
Full Text: DOI
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