Theoretical analysis demonstrates explicit stability bounds in additive return models, highlighting the necessity of weighted-variation metrics for jump processes.
We prove explicit stability bounds for CRRA portfolio functionals in one-dimensional stochastic-exponential additive return models with bounded no-short-sale portfolio fractions. The main estimate compares the Hamiltonians through [Formula: see text] perturbations of the drift and diffusion coefficients and through total variation of the finite weighted kernels [Formula: see text], where [Formula: see text]. This weight is tailored to the CRRA integrand: Compensated small jumps are quadratic, while large positive jumps contribute at order [Formula: see text]. The results yield uniform-in-control Hamiltonian convergence, a value bound, and an [Formula: see text] optimizer bound under strong concavity. For the associated CRRA problem, deterministic pointwise maximizers are optimal among all bounded predictable controls. A rare-large-jump example shows that UCP convergence and even a vanishing unweighted variation for finite jump kernels need not imply value stability; a complementary small-jump example shows that both exponents in [Formula: see text] are sharp.
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Aoyagi et al. (2026) studied this question.
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