• The Pure and Applied Mathematics
• /
• v.20 no.4
• /
• pp.287-298
• /
• 2013

A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property discouraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which generalize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.723-732
• /
• 2008

In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug's formula on the concrete Wiener measure.

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.25-34
• /
• 2020

The classical limit theorems like strong law of large numbers, central limit theorems and law of iterated logarithms are fundamental theories in probability and statistics. These limit theorems are proved under additivity of probabilities and expectations. In this paper, we investigate strong law of large numbers under sub-linear expectation which generalize the classical ones. We give strong law of large numbers under sub-linear expectation with respect to the partial sums and some conditions similar to Petrov's. It is an extension of the classical Chung type strong law of large numbers of Jardas et al.'s result. As an application, we obtain Chung's strong law of large number and Marcinkiewicz's strong law of large number for independent and identically distributed random variables under the sub-linear expectation. Here the sub-linear expectation and its related capacity are not additive.

• Journal of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.359-381
• /
• 2020

In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued Lévy's martingale convergence theorem are proved by using the Slice and the linear topologies.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.385-396
• /
• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.485-489
• /
• 2010

A family of continuous probability distribution has been characterized through the difference of two conditional expectations, conditioned on a non-adjacent record statistic. Also, a result based on the unconditional expectation and a conditional expectation is used to characterize a family of distributions. Further, some of its deductions are also discussed.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.27-33
• /
• 2008

The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.699-705
• /
• 1999

Given a probability space and a subsigma algebra A, each measure equivalent to the probability measure generates a different conditional expectation operator. We characterize those which act boundedly on the original $L^2$ space, and show there are sufficiently many such conditional expectations to generate the commutant of $L^{\infty}$ (A).

• East Asian mathematical journal
• /
• v.31 no.4
• /
• pp.393-420
• /
• 2015

The expectation and confirmation emerging as one of problem-solving strategies in the elementary school is a strategy that does not limited in the elementary school but used in the middle and high school. This strategy inevitably requires a process of adjustment that affected by the earlier expectation. Such an adjustment raised expectation and confirmation to one of effective problem-solving strategies. The adjustment is especially important to carry out the strategy effectively. The aim of this study was to conduct basic research on cognitive characteristics appearing to students when they carried out the expectation and confirmation strategy. We investigated and analyzed this in term of adjustment of expectation. To do this, we examined 50 5th graders' response in three kinds of word problems and interviewed with 4 participants who is using the expectation and confirmation strategy. The interview was conducted by using the items or solutions used in the test. From this, we tried to check students' cognitive characteristics and recognition on it's value. Furthermore we proposed the pedagogical implications associated with these results.

• The Pure and Applied Mathematics
• /
• v.22 no.4
• /
• pp.333-342
• /
• 2015

We show that the set of priors in the representation of Choquet expectation is the one of equivalent martingale measures under some conditions, when given capacity is submodular. It is proven via Peng’s g-expectation and related topics.