Abstract. This paper is concerned with using stochastic approximation and optimization methods for stock liquidation decision making and option pricing. For stock liquidation problem, we present a class of stochastic recursive algorithms, and make comparisons of performances using stochastic approximation methods and that of certain commonly used heuristic methods, such as moving averaging method and moving maximum method. Stocks listed in NASDAQ are used for making the comparisons. For option pricing, we design stochastic optimization algorithms and present numerical experiments using data derived from Berkeley Options Data Base. An important problem in these studies concerns the rate of convergence taking into consideration of bias and noise variance. In an effort to ascertain the convergence rates incorporating the computational efforts, we use a Liapunov function approach to obtain the desired convergence rates. Variants of the algorithms are also suggested.
We begin this paper by introducing the Linnik distributions in both the univariate and multivariate case. An overview of simulation methods and two estimation procedures for the multivariate Linnik distribution are presented. Experiments demonstrating the accuracy of the procedures are also included. Then a novel multivariate Linnik copula is derived. The primary focus of this part of work is on simulation and estimation procedures for this copula, applying existing algorithms for simulation and estimation procedures for the multivariate Linnik distribution derived in the prior section. Several theoretical properties of the copula in relation to different dependence metrics are derived.
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