 Projection PricingD. G. Luenberger Journal of Optimization Theory and Applications, 2001, vol. 109, issue 1, No 1, 25 pages Abstract: Abstract A significant problem in modern finance theory is how to price assets whose payoffs are outside the span of marketed assets. In practice, prices of assets are often assigned by using the capital asset pricing model (CAPM). If the market portfolio is efficient, the price obtained this way is equal to the price of an asset whose payoff, viewed as a vector in a Hilbert space of random variables, is projected orthogonally onto the space of marketed assets. This paper looks at the pricing problem from this projection viewpoint. It is shown that the results of the CAPM formula are duplicated by a formula based on the minimum-norm portfolio, and this pricing formula is valid even in cases when there is no efficient portfolio of risky assets. The relation of the pricing to other aspects of projection are also developed. In particular, a new pricing formula, called the correlation pricing formula, is developed that yields the same price as the CAPM, but is likely to be more accurate and more convenient than the CAPM in some cases. Keywords: asset pricing; projection theorem; correlation pricing; Hilbert space (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:109:y:2001:i:1:d:10.1023_a:1017596419383 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull More articles in Journal of Optimization Theory and Applications from Springer |
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