Úlohy stochastické optimalizace ve financích

Rusý, Tomáš

Title: Asset-Liability Management: Application of Stochastic Programming with Endogenous Randomness and Contamination Author: RNDr. Tomáš Rusý Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, PhD., Department of Probability and Mathematical Statistics Abstract: This thesis discusses a stochastic programming asset-liability management model that deals with decision-dependent randomness and a subsequent contamination analysis. The main model focuses on a pricing problem and the connected asset- liability management problem describing the typical life of a consumer loan. The endogeneity stems from the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepay- ment which are all affected by the company's decision on interest rate of the loan. Another important factor, which plays a major role for liabilities, is the price of money in the market. There, we focus on the scenario generation procedure and develop a new calibration method for estimating the Hull-White model [Hull and White, 1990] under the real-world measure. We define the method for the gen- eral class of one-factor short-rate models and perform an extensive analysis to assess the estimation performance and...

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