Dynamically consistent investment under model uncertainty: the robust forward criteria

Sigrid Källblad (), Jan Obłój () and Thaleia Zariphopoulou ()
Additional contact information
Sigrid Källblad: Technische Universität Wien
Jan Obłój: University of Oxford
Thaleia Zariphopoulou: The University of Texas at Austin

Finance and Stochastics, 2018, vol. 22, issue 4, No 4, 879-918

Abstract: Abstract We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences. We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and Žitković (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk λ ˆ $\hat{\lambda}$ 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 λ ˆ $\hat{\lambda}$ and with the leverage being proportional to the investor’s confidence in her estimate.

Keywords: Robust forward criteria; Optimal investment; Model uncertainty; Ambiguity aversion; Dynamic consistency; Time-consistency; Duality theory; 91B16; 91G10; 91B06; 91G80; 49N15; 62C20 (search for similar items in EconPapers)
JEL-codes: D81 G11 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (17)

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DOI: 10.1007/s00780-018-0368-4

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