Open Access
June 2017 The pricing of contingent claims and optimal positions in asymptotically complete markets
Michail Anthropelos, Scott Robertson, Konstantinos Spiliopoulos
Ann. Appl. Probab. 27(3): 1778-1830 (June 2017). DOI: 10.1214/16-AAP1246

Abstract

We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semimartingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well-defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to large deviations theory, and in particular, the celebrated Gärtner–Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, models of large markets with vanishing trading restrictions and the Black–Scholes–Merton model with either vanishing default probabilities or vanishing transaction costs. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models.

Citation

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Michail Anthropelos. Scott Robertson. Konstantinos Spiliopoulos. "The pricing of contingent claims and optimal positions in asymptotically complete markets." Ann. Appl. Probab. 27 (3) 1778 - 1830, June 2017. https://doi.org/10.1214/16-AAP1246

Information

Received: 1 September 2015; Revised: 1 September 2016; Published: June 2017
First available in Project Euclid: 19 July 2017

zbMATH: 06775362
MathSciNet: MR3678485
Digital Object Identifier: 10.1214/16-AAP1246

Subjects:
Primary: 60F10 , 60H10 , 91G99

Keywords: incomplete markets , Indifference pricing , large position size , utility functions

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 3 • June 2017
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