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On Approximating the Minimum Initial Capital of Fire Insurance with the Finite-time Ruin Probability using a Simulation Approach

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Supawan Khotama, Thotsaphon Thongjunthug, Kiat Sangaroon, Watcharin Klongdee

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This paper considers the discrete time surplus process in the case of fire insurance

given by U0=u,Un=Un-1+cZn-Yn, where {Yn,n ≥ 1} is the claim severity process, {Zn,n ≥ 1}

is the inter-arrival process, c is the premium rate, and U0=u ≥ 0 is the initial capital. The

claim severities and the inter-arrival time are provided by the Thai Reinsurance Public Co.,

Ltd. In addition, we assume that {Yn,n ≥ 1} and {Zn,n ≥ 1} are independent and identically

distributed, Yn has Weibull distribution and Zn has Poisson distribution. By using the

maximum likelihood estimator method, we find that Yn~Weibull (0.8484,30.5396) and

Zn~Poisson (37.8958). Finally, we approximate the finite-time ruin probability for one year

by a simulation approach, and use the logarithmic regression to approximate the minimum

initial capital corresponding to the quantities of risk α = 0.01 and 0.05, respectively.

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ruin probability; insurance; minimum initial capital; surplus process