Optimal Consumption and Portfolio Choice with Ambiguity

Abstract

We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying the worst-case measure. Our setup also allows to consider interest rate uncertainty; we show that under some robust parameter constellations, the investor optimally puts all his wealth into the asset market, and does not save or borrow at all.

Horizon-unbiased investment with ambiguity

“…Such premium-based rule (4.28) on the conservative belief towards the mean return is consistent with the rule proposed by Chong & Liang (2018) and Lin & Riedel (2014). Chong & Liang (2018) propose to select the worst-case scenario of the mean return in a feedback form associated with the position on risky assets, i.e., the long and short positions correspond to µ and µ, respectively.…”

“…Chong & Liang (2018) propose to select the worst-case scenario of the mean return in a feedback form associated with the position on risky assets, i.e., the long and short positions correspond to µ and µ, respectively. In the classical framework, the selection of worst-case mean return dependents on the investor's position on the risky asset, as argued by Lin & Riedel (2014) that nature decides for a low drift if an investor takes a long position, and for a high drift if an investor takes a long position. However, the rule (4.28) is not given in a feedback form associated with an investor's position, but directly related to the market situations and the investor's utility risk premium.…”

Robust utility maximisation in markets with transaction costs

“…If only volatility uncertainty is considered, then the family of laws is mutually singular. See [22] and [6] about treatments for similar models. Remark 2.3.…”

“…The robust model in this paper, similar to the ones introduced in [6], [25], [22], assumes that there is a parametrization for the uncertain dynamics of risky assets. However, as we will see below, no specific assumption is made about the parametrization and an arbitrary index set is permitted.…”

Nonconcave robust optimization with discrete strategies under Knightian uncertainty

“…There, concavity is assumed on the maps Ψ(ω, ·) for every ω ∈ Ω. For more results concerning the robust utility maximization problem in a nondominated framework, we refer to [20,2,6,8,11,14,16,17,18,31]. For examples of robust optimal stopping problem, we refer to [3,4,21,12].…”