• Title, Summary, Keyword: stochastic comparison

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MEAN-FIELD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MARKOV CHAINS

  • Lu, Wen;Ren, Yong
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.17-28
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    • 2017
  • In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

THE SOLUTIONS OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS

  • Han, Baoyan;Zhu, Bo
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1143-1155
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    • 2011
  • In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.

A Note on the Stochastic Comparison in Production Yield Management (생산 수율 관리 문제와 확률적 비교)

  • Park, Kyungchul
    • Journal of Korean Institute of Industrial Engineers
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    • v.40 no.5
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    • pp.477-480
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    • 2014
  • The single-period production inventory control problem under random yield is considered to analyze the impact of the yield characteristics on the firm's profit. We use the stochastic comparison as a main vehicle to compare the profits resulted under different random yields. Commonly used stochastic orderings are addressed with an analysis of their implications on the firm's profit. Moreover, a distribution-free bound on the profit is derived.

Stochastic Comparisons of Order Statistics

  • Kim, Song-Ho
    • Journal of the Korean Statistical Society
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    • v.22 no.1
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    • pp.13-25
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    • 1993
  • The purpose of this paper is to investigate the properties of order statistics under various stochastic relations. We study the stochastic comparison of order statistics in a single sample. And we consider two sample case too. For example, F(t) > G9t) for t > 0 when X and Y are random variables symmetric about 0, with c.d.f.s F and G. Two examples are provided.

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Stochastic finite element analysis of structural systems with partially restrained connections subjected to seismic loads

  • Cavdar, Ozlem;Bayraktar, Alemdar;Cavdar, Ahmet;Kartal, Murat Emre
    • Steel and Composite Structures
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    • v.9 no.6
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    • pp.499-518
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    • 2009
  • The present paper investigates the stochastic seismic responses of steel structure systems with Partially Restrained (PR) connections by using Perturbation based Stochastic Finite Element (PSFEM) method. A stiffness matrix formulation of steel systems with PR connections and PSFEM and MCS formulations of structural systems are given. Based on the formulations, a computer program in FORTRAN language has been developed, and stochastic seismic analyses of steel frame and bridge systems have been performed for different types of connections. The connection parameters, material and geometrical properties are assumed to be random variables in the analyses. The Kocaeli earthquake occurred in 1999 is considered as a ground motion. The connection parameters, material and geometrical properties are considered to be random variables. The efficiency and accuracy of the proposed SFEM algorithm are validated by comparison with results of Monte Carlo simulation (MCS) method.

Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

  • Dong, Yongpeng;Fan, Shengjun
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.985-999
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    • 2018
  • This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

COMPARISON OF STOCHASTIC VOLATILITY MODELS: EMPIRICAL STUDY ON KOSPI 200 INDEX OPTIONS

  • Moon, Kyoung-Sook;Seon, Jung-Yon;Wee, In-Suk;Yoon, Choong-Seok
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.209-227
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    • 2009
  • We examine a unified approach of calculating the closed form solutions of option price under stochastic volatility models using stochastic calculus and the Fourier inversion formula. In particular, we review and derive the option pricing formulas under Heston and correlated Stein-Stein models using a systematic and comprehensive approach which were derived individually earlier. We compare the empirical performances of the two stochastic volatility models and the Black-Scholes model in pricing KOSPI 200 index options.

Stochastic Comparisons of Markovian Retrial Queues

  • Shin, Yang-Woo;Kim, Yeong-Cheol
    • Journal of the Korean Statistical Society
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    • v.29 no.4
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    • pp.473-488
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    • 2000
  • We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes(C(t), N(t)) representing the number of customers C(t) in the service facility and one N(t) in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

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