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تسجيل مستخدم جديدConvergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets
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We examine Kreps (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that approach the BSM economy in a natural sense: The $n$th discrete-time economy is generated by a scaled $n$-step random walk, based on an unscaled random variable $zeta$ with mean zero, variance one, and bounded support. We confirm Kreps conjecture if the consumers utility function $U$ has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function $U$ with asymptotic elasticity equal to 1, for $zeta$ such that $E[zeta^3] > 0.$
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