• 응용통계연구
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• 제22권1호
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• pp.59-73
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• 2009

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will propose an outside floating-strike lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at some percentage of the lowest (or highest) price of the other underlying asset. In addition, this paper will derive explicit pricing formulas for these outside floating-strike lookback options. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples will be discussed.

• 응용통계연구
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• 제21권3호
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• pp.485-495
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• 2008

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will present explicit pricing formulas for these floating-strike lookback options with flexible monitoring periods. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying asset pays dividends continuously at a rate proportional to its price.

• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.819-835
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• 2012

A floating-strike lookback call (or put) option gives the holder the right to buy (or sell) at some percentage of the lowest (or highest) price of the underlying asset. This paper will propose an outside lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at its guaranteed floating-strike price that is some percentage times the smaller (or the greater) of a specific guaranteed amount and the lowest (or highest) price of the other underlying asset. In addition, this paper derives explicit pricing formulas for these outside lookback options. Section 3 and Section 4 assume that the underlying assets pay no dividends. In contrast, Section 5 derives explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples are also discussed.

• 대한수학회논문집
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• 제17권1호
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• pp.15-20
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• 2002

We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.105-122
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• 2023

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by Clifford multiplication over the standard sphere in odd dimension. In the even dimensional case, we give the spectra of the square of such operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form cases, respectively. We also give eigenvalue formulas for the conformally invariant differential operators of all odd orders on the subbundle of the bundle of spinor-valued forms that are annihilated by Clifford multiplication in both even and odd dimensions on the sphere.

• 대한수학회지
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• 제57권6호
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• pp.1407-1433
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• 2020

Parts I-IV showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope. Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by Kotššovec. We prove some of Kotššovec's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.

• 대한수학회지
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• 제49권1호
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• pp.69-83
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• 2012

In this note, we present certain circular domain, named Forelli-Rudin construction or Hua construction, which is built on Cartan domains. We compute the explicit Bergman kernel for it and get the corresponding weighted Bergman kernel on its base.

• 대한수학회지
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• 제48권2호
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• pp.267-288
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• 2011

In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group $SO^-$(2n, q). Here q is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formulas for even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups $O^-$(2n, q).

• 응용통계연구
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• 제25권5호
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• pp.813-820
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• 2012

A surplus process with two types of claims is considered, where Type I claims occur more frequently, however, their sizes are smaller stochastically than Type II claims. The ruin probabilities of the surplus caused by each type of claim are obtained by establishing integro-differential equations for the ruin probabilities. The formulas of the ruin probabilities contain an infinite sum and convolutions that make the formulas hard to be applicable in practice; subsequently, we obtain explicit formulas for the ruin probabilities when the sizes of both types of claims are exponentially distributed. Finally, we show through a numerical example, that Type II claims have more impact on the ruin probability of the surplus than Type I claims.

• 대한수학회논문집
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• 제29권3호
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• pp.415-420
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• 2014

We give explicit formulas, without using the Poisson integral, for the functions that are C-harmonic on the unit disk and restrict to a prescribed polynomial on the boundary.