• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.863-875
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• 2010

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권2호
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• pp.115-128
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• 2013

The optimal portfolio selection problem under inflation risk and subsistence constraints is considered. There are index bonds to invest in financial market and it helps to hedge the inflation risk. By applying the martingale method, the optimal consumption rate and the optimal portfolios are obtained explicitly. Furthermore, the quantitative effect of inflation risk and subsistence constraints on the optimal polices are also described.

• 충청수학회지
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• 제33권1호
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• pp.103-112
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• 2020

This paper investigates the portfolio selection problem with flexible labor choice and stochastic income flow where the unit wage flow is governed by a stochastic process. The agent optimally chooses consumption, investment, and labor supply. We derive the closed-form solution by applying a martingale method even with the stochastic income flow.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.359-364
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• 2005

This paper considers a specification test of conditional Poisson regression model for time series count data. Although conditional models for count data have received attention and proposed in several ways, few studies focused on checking its adequacy. Motivated by the test of martingale difference assumption, a specification test via Ljung-Box statistic is proposed in the conditional model of the time series count data. In order to illustrate the performance of Ljung- Box test, simulation results will be provided.

• 대한수학회보
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• 제29권1호
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• pp.145-151
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• 1992

• Kyungpook Mathematical Journal
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• 제32권3_spc호
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• pp.369-374
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• 1992

• 충청수학회지
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• 제28권1호
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• pp.109-117
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• 2015

We consider the relative entropy for two R-CGMY processes, which are CGMY processes with Y equal to 1, to choose an equivalent martingale measure (EMM) when the underlying asset of a derivative follows a R-CGMY process in the financial market. Since the R-CGMY process leads to an incomplete market, we have to use a proper technique to choose an EMM among a variety of EMMs. In this paper, we derive the closed form expression of the relative entropy for R-CGMY processes.

• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.453-458
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• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.489-497
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• 2000

The M/M/1 queue with impatient customers is studied. Impatient customers wait for service only for limited time K/0 and leave the system if their services do not start during that time. Notice that in the analysis of virtual waiting time, the impatient customer can be considered as the customer who enters the system only when his/her waiting time does not exceed K. In this paper, we apply martingale methods to the virtual waiting time and obtain the expected period from origin to the point where the virtual waiting time crosses over K or reaches 0, and the variance of this period. With this results, we obtain the expected busy period of the queue, the distribution, expectation and variance of the number of times the virtual waiting time exceeding level K during a busy period, and the probability of there being no impatient customers in a busy period.