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A note on the worst case approach for a market with a stochastic interest rate

Volume 45 / 2018

Dariusz Zawisza Applicationes Mathematicae 45 (2018), 151-160 MSC: 91G80, 91G10, 91A15, 91A25, 49N90, 49N60. DOI: 10.4064/am2348-2-2018 Published online: 23 October 2018

Abstract

We solve a robust optimization problem and show an example of a market model for which the worst case measure is not a martingale measure. In our model the instantaneous interest rate is determined by the Hull–White model and the investor employs the HARA utility to measure his satisfaction. To protect against the model uncertainty he uses the worst case measure approach. The problem is formulated as a stochastic game between the investor and the market. PDE methods are used to find a saddle point and a precise verification argument is provided.

Authors

  • Dariusz ZawiszaFaculty of Mathematics and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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