Ambiguity volatility and credit risk

Endowed with equal wealth, risk- and ambiguity-averse investors decide whether to optimally buy or sell credit protection on the underlying referenced debt.
Each investor’s decision depends on their relative sensitivity to risk and ambiguity.

The result of a positive effect of ambiguity on credit spreads depends on the perspective of an investor who considers a drop in the value of the underlying asset to be unfavorable.
However, as discussed above, a drop in asset value may be considered favorable if the investor has a short position in the asset.

Under ambiguity in terms of the mean return, there is nonparticipation in the risky asset market.
However, in absence of ambiguity ( μ = μ 0), an investor will always participate in the risky asset market unless r = μ 0 + g ( t) σ 2, as shown in Fig. 1.

Ambiguity only in terms of the mean return is referred to as the case where the mean return is ambiguous, but the volatility is known.
For the sake of simplicity, we assume that σt is known as a positive constant σ, while μ t ∈ [ μ, μ ¯] with 0 < μ ≤ μ ¯, for t ≥ 0.