Merton Investment Problems in Finance and Insurance for the Hawkes-based Models

TL;DR

This paper develops solutions for Merton optimal investment problems within new Hawkes process-based models in finance and insurance, providing novel models and optimal strategies for portfolios and insurance capital.

Contribution

It introduces new Hawkes-based models for finance and insurance and derives optimal investment strategies within these models.

Findings

Derived explicit solutions for investment problems in Hawkes-based models

Introduced novel Hawkes process models for finance and insurance applications

Provided insights into optimal portfolio and capital management in complex stochastic environments

Abstract

We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance, 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) of an insurance company with the amount of claims described by the risk model based on GCHP. 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.