The robust Merton problem of an ambiguity averse investor

Abstract

We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. The novelty is that confidence is here represented using ellipsoidal uncertainty sets for the drift, given a volatility realization. This specification affords a simple and concise analysis, as the optimal portfolio allocation policy is shaped by a rescaled market Sharpe ratio, computed under the worst case volatility. The result is based on a max-min Hamilton-Jacobi-Bellman-Isaacs PDE, which extends the classical Merton problem and reverts to it for an ambiguity-neutral investor.

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.…”

“…After these preparations, we turn to the main arguments. Assumption 3.5, (7) and (6) imply that u θ (x) is finite for each θ and so is u(x). Let H n ∈ A(x), n ∈ N be a maximizing sequence, i.e.…”

Good deal hedging and valuation under combined uncertainty about drift and volatility

“…e.g., Garlappi et al (2007) or Biagini and Pınar (2017). We denote by : [0, T ] × R n the correspondence (set-valued mapping)…”

Robust Utility Maximization With Lévy Processes

“…A saddle point is found and analyzed, again by dynamic programming arguments. Recently, Biagini and Pinar (2015) also construct a saddle point in a setting where the uncertainty in the drift may depend on the realization of the volatility in a specific way. Finally, Fouque, Pun, and Wong (2014) consider a stochastic volatility model with uncertain correlation (but known drift) and describe an asymptotic closed-form solution.…”