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A SURVEY ON AMERICAN OPTIONS: OLD APPROACHES AND NEW TRENDS
Ahn, Se-Ryoong,Bae, Hyeong-Ohk,Koo, Hyeng-Keun,Lee, Ki-Jung Korean Mathematical Society 2011 대한수학회보 Vol.48 No.4
This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.
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OPTIMAL CONSUMPTION AND SLUTSKY EQUATION WITH EPSTEIN-ZIN TYPE PREFERENCE
SE RYOONG AHN,HYENG KEUN KOO 한국산업응용수학회 2012 Journal of the Korean Society for Industrial and A Vol.16 No.2
In this paper we conduct comparative statics for optimal consumption and portfolio selection of an agent who has a utility function of Epstein and Zin type. We derive the Slutsky equations and decompose the total effects of changes into the substitution effects and the income effects. We identify the role of the elasticity of intertemporal substitution and the coefficient of relative risk aversion.
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