Optimal stopping problems and pricing of american exotic options = 최적 멈춤 문제와 아메리칸 이색 옵션 가격 산정

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We find closed form formulas for the value functions of the several types of American lookback spread option through solving optimal stopping problems of running maximum and minimum of an underlying process. First of all, we provide formulas for fixed strike, floating strike lookback options and lookback spread option whose payoff is the difference of the running maximum and minimum prices of a single asset. Therefore, an optimal stopping problem related to both maximum and minimum is posed. Using the monotonicity of the maximum and minimum processes we show that the spread option is equivalent to some fixed strike options on some domains, find the exact form of the optimal stopping region, and obtain the solution of the resulting partial differential equations. We also solve an optimal stopping problem whose gain is the ratio between the maximum and minimum. Finally, we address the optimal selling strategy for an investor who has regret on the maximum value.
Advisors
Choe, Geon Horesearcher최건호researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2020
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2020.8,[iv, 60 p. :]

Keywords

Optimal stopping problem▼aFree boundary problem▼aAmerican option▼aLookback option▼aMaximum and minimum processes▼aStochastic control; 최적 멈춤 문제▼a자유 경계 문제▼a아메리칸 옵션▼a룩백 옵션▼a최댓값과 최솟값 과정▼a확률적 제어

URI
http://hdl.handle.net/10203/284357
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=924358&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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