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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.

MSC:
91G10 Portfolio theory
90C90 Applications of mathematical programming
90C15 Stochastic programming
Software:
MINLP
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