Valuation Unit-Linked Life Insurance with Continuous-Installment Premium

In this paper, we present a two-phase approach to value unit-linked life insurance which the premium is paid continuously instead of up-front prior to a fixed time. At or before maturity, the policyholder withdraw a constant cash flow at proportion withdrawal rate from the corresponding sub-account regardless of the performance of the capital market. Under the unual assumptions, we derive the sub-account value process and build the payment model as well the withdrawal one. By using arbitrage-free principle and the two-phase method to analyze the discounted expect payoff, we achieve the pricing partial differential equations and deduce the fair policy value.