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Option pricing in an incomplete market with continuous asset price process. (English) Zbl 0903.90010

Summary: The problem of hedging contingent claims by portfolios constrained to take values in a given convex, closed subset of \({\mathcal R}^m\) in an incomplete market is studied. By extending the pair of portfolio and consumption to a triple of portfolio, extra-investment and consumption, an interval of arbitrage-free prices of a given contingent claim is obtained.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B62 Economic growth models
93E20 Optimal stochastic control
60H30 Applications of stochastic analysis (to PDEs, etc.)
60G44 Martingales with continuous parameter
91B24 Microeconomic theory (price theory and economic markets)
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