Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment

Maxim Bichuch ()

Finance and Stochastics, 2014, vol. 18, issue 3, 694 pages

Abstract: We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost ε>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307–324, 1997 ), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of $\varepsilon^{\frac{1}{3}}$ in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of $\varepsilon^{\frac{2}{3}}$ . In both cases, we also obtain a “nearly optimal” strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Transaction costs; Optimal control; Asymptotic analysis; Utility maximization; Option pricing; 91G80; 60H30; G13 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00780-014-0233-z (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:18:y:2014:i:3:p:651-694

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-014-0233-z

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().