The valuation of cash-flows in the presence of dividend barriers

A subject often recurring in financial and actuarial papers is the pricing of stocks and securities when the rate of return is stochastic. In most cases, the stocks considered are assumed not to pay out any dividend. In the present contribution we show how it is possible to obtain upper and lower bounds for the (distribution of the) accumulated value of a cash-flow in the presence of dividend barriers at a future time t, when the logarithm of the stock price is modelled by means of a Wiener process. 1 Description of the problem For t ≥ 0, let S(t) denote the price of a non-dividend paying stock or security at time t. We then have S(t) = S0eX(t), (1) assuming that there exists a stochastic process X(t) with stationary and independent increments, representing the stochastic continuous compounded rate of return over the period [0, t]. In the classical model, stock prices are assumed to be log-normally distributed, and the process X(t) is a Wiener process. ∗ University of Antwerp, Belgium † K.U.Leuven, Belgium and University of Amsterdam, the Netherlands ‡ K.U.Leuven, Belgium and University of Amsterdam, the Netherlands § K.U.Leuven, Belgium ¶ University of Amsterdam, the Netherlands