We aim at generalizing the celebrated portfolio optimization problem "à la Merton", where the asset evolution is steered by a self-exciting jump-diffusion process. We first define the rigorous mathematical framework needed to introduce the stochastic optimal control problem we are interesting in. Then, we provide a proof for a specific version of the Dynamic Programming Principle (DPP) with respect to the
general class of self-exciting processes under study. After, we state the Hamilton-Jacobi-Bellman (HJB) equation, whose solution gives the value function for the corresponding optimal control problem.
The resulting HJB equation takes the form of a Partial-Integro Differential Equation (PIDE), for which we prove both existence and uniqueness for the solution in the viscosity sense. We further derive a suitable numerical scheme to solve the HJB equation corresponding to the portfolio optimizationproblem. To this end, we also provide a detailed study of solution dependence on the parameters of the problem. The analysis is performed by calibrating the model on ENI asset levels during the COVID-19 worldwide breakout. In particular, the calibration routine is based on a sophisticated Sequential Monte Carlo algorithm.
| Identifer | oai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/339574 |
| Date | 27 April 2022 |
| Creators | Veronese, Andrea |
| Contributors | Veronese, Andrea, Di Persio, Luca |
| Publisher | Università degli studi di Trento, place:TRENTO |
| Source Sets | Università di Trento |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | lastpage:1, numberofpages:92 |
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