Forward indifference valuation for dynamically incoming projects

Haoran Wang

doi:10.3934/puqr.2024011

Article Contents

2024, Volume 9, Issue 2: 219-234. Doi: 10.3934/puqr.2024011

This issue Previous Article Rank-dependent predictable forward performance processes Next Article Optimal liquidation with dynamic parameter updating: A forward approach

Forward indifference valuation for dynamically incoming projects

Haoran Wang

444 Warren Street, Jersey City, New Jersey, 07302, USA

Received: December 2023

Accepted: May 16, 2024

Early access: June 2024

Published: June 2024

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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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.

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Mathematics Subject Classification: 60H30, 91G30.

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Figure 1. Model inputs for relative indifference valuation of the second project

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