Robust utility maximization for a diffusion market model with misspecified coefficients

Abstract

The paper studies the robust maximization of utility from terminal wealth in a diffusion financial market model. The underlying model consists of a tradable risky asset whose price is described by a diffusion process with misspecified trend and volatility coefficients, and a non-tradable asset with a known parameter. The robust functional is defined in terms of a utility function. An explicit characterization of the solution is given via the solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation.

Robust utility maximisation in markets with transaction costs

“…More recently, the non-dominated problem has also been studied in various contexts. For instance, [35] investigated a compact set of possible drift and volatility coefficients and tackled the robust problem by solving an associated Hamilton-Jacobi-Bellman equation. In [24], where volatility coefficients are uncertain over a compact set and the drift is known, the theory of BSDEs is applied.…”

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

“…Likewise, we are aware of only few recent articles on the related problem of expected utility maximization under uncertainty about both drifts and volatilities (cf. Tevzadze et al 2013;Biagini and Pınar 2017;Neufeld and Nutz 2016) some of which achieve quite explicit results for models with specific parametric structure. Among many interesting contributions on utility optimization under only one type of uncertainty, see for instance Chen and Epstein (2002), Quenez (2004), Garlappi et al (2007), Schied (2007) or Øksendal and Sulem (2014) for (dominated) uncertainty solely about drifts, or Matoussi et al (2015) and Hu et al (2014b) for ambiguity solely about volatilities but not about drifts.…”

Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

“…Assume that T is a large enough number. For the logarithm utility case, the optimal consumption c * t = x * c,L (q L (t)), t ∈ [ 0, T ], is a deterministic process, with x * c,L (·) and q L (·) given respectively in (29) and (34). Moreover, the optimal consumption c * t is summarized in Table 5 3 .…”

“…First, it is clear that the solution of ODE (19) takes the form (34). From (29), we know that x * c,L (x q ) is nonincreasing with respect to x q . Moreover, the expression (34) implies that q L (·) is nondecreasing with respect to t when ρ ≥ λ, and nonincreasing with respect to t when ρ ≤ λ.…”