Forward indifference valuation for dynamically incoming projects

Abstract

Classical indifference valuation, a widely studied approach in incomplete markets, uses critically the a priori knowledge of the characteristics (arrival, maturity, payoff structure) of the projects in consideration. This assumption, however, may not accommodate realistic scenarios in which projects, not initially anticipated, arrive at later times. To accommodate this, we employ forward indifference valuation criteria, which by construction are flexible enough to adapt to such “non-anticipated” cases while yielding time-consistent indifference prices. We consider and analyze in detail two representative cases: valuation adjustments due to incoming non-anticipated project and the relative forward indifference valuation of new projects in relation to existing ones.

Keywords

Forward indifference valuation / Dynamically incoming projects / Indifference pricing / Relative forward indifference valuation / Predictable forward criteria / Adaptive forward criteria / Risk decomposition

Acknowledgements

The work is part of the author’s Ph.D. Thesis at the University of Texas at Austin. It was presented at the 4th Young Researchers Meeting on BSDEs, Nonlinear Expectations and Mathematical Finance, SJTU, China, and the conference on Financial and Economic Applications, IMA, University of Minnesota. The author would like to thank T. Zariphopoulou, G. Zitkovic, X.Y. Zhou, and L. Zhang for fruitful comments and suggestions.

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