| Abstract: |
| We study the optimal timing for a firm to invest in cybersecurity technology while managing cyber risk through insurance. Cyber losses are modeled as a jump process to capture fat-tailed behavior, and investment costs evolve stochastically via a compound Poisson process due to technological uncertainty. The firm aims to minimize total expected costs, including losses, investment, and insurance premiums. By formulating an optimal stopping problem and solving the corresponding Hamilton-Jacobi-Bellman equations, we obtain semi-closed-form solutions for the value function and optimal strategies. Numerical examples illustrate how key factors, such as loss intensity, insurance coverage, and cost volatility, affect investment timing and risk-sharing decisions. |
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