Lunch Seminar Mathematics & Statistics (LSE) - 2020/2021

Interviene: Milos Kopa, Charles University in Prague

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Abstract 

We present a stochastic programming asset–liability management model which deals with decision-dependent randomness. The model focuses on a pricing problem and the subsequent asset–liability management problem describing the typical life of a consumer loan. Such problems are frequently tackled by many companies, including multinationals. When doing so, they must consider numerous factors. These factors include the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepayment. The randomness associated with these factors have a clear relationship with the offered interest rate of the loan which is the company’s decision and thus, induces decision-dependent randomness. Another important factor, which plays a major role for liabilities, is the price of money in the market. This is determined by the market interest rates. We captured their evolution in the form of a scenario tree. In summary, we formulated a non-linear, multi-stage stochastic program with decision-dependent randomness, which spanned the lifetime of a typical consumer loan. Its solution showed us the optimal decisions that the company should make. In addition, we performed a sensitivity analysis demonstrating the results of the model for various parameter settings that described different types of customers. Finally, we discuss the losses caused if companies do not act in the optimal way.