This paper studies stability of the exponential utility maximization when there are small variations on agent's utility  . Two settings are studied . First, in a general semimartingale model where random endowments are present, there is a sequence of utilities defined on R converging to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal terminal wealth and optimal investment strategies are obtained, their rate of convergence are  determined. Stability of utility-based pricing is also discussed . Second, there is a sequence of utilities defined on R_+ each of which is comparable to a power utility whose relative risk aversion converges to infinity . Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in M. Nutz, Probab. Theory Relat. Fields, 152, 2012, by allowing general utilities in the converging sequence .
This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function . Two settings are considered . First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on R converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payoffs and optimal investment strategies are obtained, their rate of convergence are also determined. Stability of utility-based pricing is studied as an application . Second, a sequence of utilities defined on R_+ converges to the exponential utility after shifting and scaling . Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in M. Nutz, Probab. Theory Relat. Fields, 152, 2012, which establishes the convergence for a sequence of power utilities .
A
function
R
studied
considered
D
there is
R
converging
converges
R
terminal wealth
payoffs
A
also
R
also discussed
studied as an application
D
there is
R
each of which is comparable to a power utility whose relative risk aversion converges to infinity
converges to the exponential utility after shifting and scaling
R
by allowing general utilities in the converging sequence
which establishes the convergence for a sequence of power utilities