A Class of Solvable Multiple Entry Problems with Forced Exits

We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when forced exits occur on the jump times of a Poisson process. F...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 79; no. 3; pp. 593 - 619
Main Author Lempa, Jukka
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2019
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Control
Economic models
Investment
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Poisson density functions
Simulation
Statistical analysis
Systems Theory
Theoretical
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Summary:We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when forced exits occur on the jump times of a Poisson process. Furthermore, we allow the investment opportunity to be subject to the risk of a catastrophe that can occur at the jumps of the Poisson process. More precisely, we attach IID Bernoulli trials to the jump times and if the trial fails, no further re-entries are allowed. Interestingly, we find in the general case that the optimal investment threshold is independent of the success probability is the Bernoulli trials. The results are illustrated with explicit examples.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-017-9449-6