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Kevin Pettersson: Stochastics and Its Application in Merton’s Problem

Bachelor thesis presentation

Time: Thu 2023-08-24 10.00 - 11.00

Location: Cramer room

Respondent: Kevin Pettersson

Supervisor: Kristoffer Lindensjö

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In this thesis, we aim to present key concepts in stochastic processes, Itô’s calculus, and stochastic dierential equations. We will give a brief overview of how stochastic dierential equations can be used in stochastic dynamic con- trol problems and how to find explicit solutions to such optimization problems. Our main focus will be to provide explicit solutions for the optimal consump- tion and investment rules in the case when the risk aversion is constant. Lastly, we will also provide concise economic interpretations and implications of such optimal consumption and investment rules.