Time-Consistent Investment Under Model Uncertainty: The Robust Forward Criteria

41 Pages Posted: 15 Nov 2013

See all articles by Sigrid Källblad

Sigrid Källblad

Vienna University of Technology

Jan Obłój

University of Oxford - Mathematical Institute; University of Oxford - Oxford-Man Institute of Quantitative Finance; University of Oxford - Saint John's College

Thaleia Zariphopoulou

University of Texas at Austin (Mathematics and IROM)

Date Written: November 14, 2013

Abstract

We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and investment horizon specification. It describes the evolution of time-consistent ambiguity averse preferences.

We first focus on establishing dual characterizations of the robust forward criteria. This offers various advantages as the dual problem amounts to a search for an infimum whereas the primal problem features a saddle-point. Our approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We then study in detail non-volatile criteria. In particular, we solve explicitly the example of an investor who starts with a logarithmic utility and applies a quadratic penalty function. The investor builds a dynamical estimate of the market price of risk and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with the investor's estimate. The leverage is proportional to the investor's confidence in her estimate.

Keywords: ambiguity averse portfolio selection, forward investment performance, time-consistency, robust control, model uncertainty, preferences amiguity

JEL Classification: G11, D81

Suggested Citation

Källblad, Sigrid and Obloj, Jan K. and Zariphopoulou, Thaleia, Time-Consistent Investment Under Model Uncertainty: The Robust Forward Criteria (November 14, 2013). Available at SSRN: https://ssrn.com/abstract=2354373 or http://dx.doi.org/10.2139/ssrn.2354373

Sigrid Källblad

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

Jan K. Obloj (Contact Author)

University of Oxford - Mathematical Institute ( email )

AWB, ROQ, Woodstock Rd
Oxford, OX2 6GG
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

University of Oxford - Saint John's College ( email )

St Giles
Oxford, Oxon OX1 3JP
United Kingdom

Thaleia Zariphopoulou

University of Texas at Austin (Mathematics and IROM) ( email )

CBA 5.202
Austin, TX 78712
United States

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