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https://doi.org/10.1007/s00780-004-0128-5
Title: | An approximation pricing algorithm in an incomplete market: A differential geometric approach | Authors: | Gao, Y. Lim, K.G. Ng, K.H. |
Keywords: | Asset pricing Cross entropy Incomplete markets Riemannian manifold |
Issue Date: | Nov-2004 | Citation: | Gao, Y., Lim, K.G., Ng, K.H. (2004-11). An approximation pricing algorithm in an incomplete market: A differential geometric approach. Finance and Stochastics 8 (4) : 501-523. ScholarBank@NUS Repository. https://doi.org/10.1007/s00780-004-0128-5 | Abstract: | The minimal distance equivalent martingale measure (EMM) defined in Goll and Rüschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geometric structure is shown on the manifold. An optimization algorithm on the Riemannian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk. © Springer-Verlag 2004. | Source Title: | Finance and Stochastics | URI: | http://scholarbank.nus.edu.sg/handle/10635/102821 | ISSN: | 09492984 | DOI: | 10.1007/s00780-004-0128-5 |
Appears in Collections: | Staff Publications |
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