Abstract
SYNOPTIC ABSTRACTIn the financial market including n risky assets with prices following the full-observed geometric-Brownian Motion model and a bank account with stochastic interest rate, we study the problem of maximizing the probability of an investor's wealth at terminal time T meeting or exceeding the value of a contingent claim C which expires at T. In this incomplete market, using an adapted duality methodology familiar in the utility maximization literatures, we characterize the optimal probability and the corresponding portfolio strategies, in the most general framework of interest rate models and contingent claims. Then we calculate in detail the case of Vasicek model for interest rate and some specific contingent claim, via the classical theorem of Time-Changing for Martingales and a generalized Cameron-Martin formula developed in the literatures.
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