An infinite-dimensional LP duality theorem
Mathematics of Operations Research
Portfolio Selection Theory with Different Interest Rates for Borrowing and Leading
Journal of Global Optimization
Mathematical and Computer Modelling: An International Journal
Optimal Timing to Purchase Options
SIAM Journal on Financial Mathematics
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The problem of pricing contingent claims or options from the price dynamics of certain securities is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market. When the market is incomplete, prices cannot be derived from the absence of arbitrage, since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolio of the basic securities. In this situation, there is a price range for the actual market price of the contingent claim. The maximum and minimum prices are studied using stochastic control methods. The main result of this work is the determination that the maximum price is the smallest price that allows the seller to hedge completely by a controlled portfolio of the basic securities. A similar result is obtained for the minimum price (which corresponds to the purchase price).