A theory of stochastic integration for bond markets

Abstract

We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.

Published at http://dx.doi.org/10.1214/105051605000000548 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• A Characterization of Hedging Portfolios for Interest Rate Contingent Claims

Cited by in corpus (5)

• Generalized integrands and bond portfolios: Pitfalls and counter examples
• On the closure in the Emery topology of semimartingale wealth-process sets
• Fractional term structure models: No-arbitrage and consistency
• No-arbitrage of second kind in countable markets with proportional transaction costs
• BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets