Likelihood Construction of Hawkes Process in Insurance Claim Settlement Process

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The construction of the likelihood equation in the point process models plays a very important role, especially to obtain a good estimator of the parameters of a model. This paper aims to construction of the likelihood of Hawkes process in solving the problem of the claim filing process in the nonlife insurance company. In the construction process, the excitation function with exponential decay is used. The result shows that the total likelihood function of the process depend on probability no claim at time t, the number of policyholder at time t, and the excitation function.