hard · Market Microstructure

Holding everything else fixed, how do these two changes affect the optimal trajectory's urgency parameter κ=√(λσ^2/eta) and the resulting expected cost-versus-variance trade-off?

1. Both raising λ and raising σ increase κ and accelerate liquidation, but only λ reflects a preference change while higher σ raises both the optimal expected impact cost and the residual timing variance the trader is fleeing.
2. Both raising λ and raising σ increase κ and accelerate liquidation identically, since the objective depends only on the product λσ^2 and the two inputs are perfectly interchangeable in every observable outcome.
3. Raising λ increases κ and front-loads the trade, but raising σ decreases κ because higher volatility widens the efficient frontier and rewards patience, so the two inputs push urgency in opposite directions.
4. Raising σ increases κ and front-loads the trade, but raising λ leaves κ unchanged because risk aversion only rescales the objective and cannot alter the Euler-Lagrange solution's curvature.

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