Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations

Mykhaylo Shkolnikov, Ronnie Sircar and Thaleia Zariphopoulou

Papers from arXiv.org

Abstract: We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae for the leading order and first order correction terms for the forward investment process and the optimal feedback portfolios. They both depend on the investor's initial preferences and the dynamically changing investment opportunities. The leading order terms resemble their time-monotone counterparts, but with the appropriate stochastic time changes resulting from averaging phenomena. The first-order terms compile the reaction of the investor to both the changes in the market input and his recent performance. Our analysis is based on an expansion of the underlying ill-posed HJB equation, and it is justified by means of an appropriate remainder estimate.

Date: 2015-04, Revised 2015-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://arxiv.org/pdf/1504.03209 Latest version (application/pdf)

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:arx:papers:1504.03209

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().