Optimal dividend and capital injection under self-exciting claims

Battle Count: 92

The paper is primarily focused on insurance risk management and actuarial science rather than quantitative trading. However, the methodology has indirect relevance: (1) the Hawkes process modeling of clustering effects is applicable to high-frequency trading and order flow modeling; (2) the reinforcement learning framework for singular stochastic control could inform optimal execution strategies; (3) the dividend/capital injection optimization parallels portfolio rebalancing problems; (4) the viscosity solution approach to HJB equations is relevant to optimal stopping problems in trading. The connection is more methodological than domain-specific.

High complexity due to: (1) two-dimensional state space with coupled jump operator in the HJB equation; (2) viscosity solution framework requiring careful discretization; (3) monotone finite-difference scheme with upwind discretization and Howard's policy iteration; (4) Ogata's thinning algorithm for Hawkes process simulation; (5) reinforcement learning with policy gradient and actor-critic methods requiring neural network training; (6) multi-line extension with mutually exciting Hawkes processes. The analytical proofs are also technically demanding, involving comparison principles and Itô calculus for jump processes.

The paper provides detailed parameter tables (Tables 1-6), grid settings, neural network architecture (2 hidden layers of 64 neurons with ReLU), learning rates, number of epochs, and Monte Carlo trajectory counts. However, no code repository is mentioned. The finite-difference scheme and RL algorithms are described algorithmically (Algorithms 1 and 2). Reproduction would require implementing Ogata's thinning algorithm for Hawkes simulation and the specific discretization scheme.