Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258196 
Year of Publication: 
2021
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 9 [Issue:] 6 [Article No.:] 108 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-13
Publisher: 
MDPI, Basel
Abstract: 
We show how to solve Merton optimal investment stochastic control problem for Hawkesbased models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) (risk process) of an insurance company with the amount of claims described by the risk model based on GCHP. The main approach in both cases is to use functional central limit theorem for the GCHP to approximate it with a diffusion process. Then we construct and solve Hamilton-Jacobi-Bellman (HJB) equation for the expected utility function. The novelty of the results consists of the new Hawkes-based models and in the new optimal investment results in finance and insurance for those models.
Subjects: 
Merton investment problem
optimal control
Hawkes process
general compoundHawkes process
LLN and FCLT
risk process
HJB equations
optimal investment in finance
optimalinvestment in insurance
diffusion approximation
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Creative Commons License: 
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Document Type: 
Article
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