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PROBABILISTIC NUMERICAL APPROACH FOR PDE AND ITS APPLICATION IN THE VALUATION OF european options

Journal of Computational Mathematics 2001年第6期19卷 591-600页

作者： Dong-sheng Wu (Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China ) 中科院系统科学所北京 100080

Presents a probabilistic numerical approach for a class of probabilistic differential equation. Application of the Brownian motion and Monte-Carlo method; Application in the valuation of european options.

关键词： Brownian motion probabilistic numerical solution european options

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A closed-form pricing formula for european options in an illiquid asset market

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Financial Innovation 2022年第1期8卷 883-900页

作者： Puneet Pasricha Song-Ping Zhu Xin-Jiang He School of Mathematics and Applied Statistics University of WollongongWollongongNSW 2522Australia School of Economics Zhejiang University of TechnologyHangzhouChina

This article addresses the problem of pricing european options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stochastic process and the sensitivity of the underlying price to market-wide liquidity is firstly introduced,so that the impact of liquidity on the underlying asset can be captured by the option pricing *** characteristic function is analytically worked out using the Feynman–Kac theorem and a closed-form pricing formula for european options is successfully derived *** numerical experiments,the accuracy of the newly derived formula is verified,and the significance of incorporating liquidity risk into option pricing is demonstrated.

关键词： european options Liquidity risk Liquidity discounting factor Characteristic function Conditional distribution

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Conditional coherent risk measures and regime-switching conic pricing

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Probability, Uncertainty and Quantitative Risk 2021年第4期6卷 267-300页

作者： Engel John C Dela Vega Robert J Elliott UniSA Business University of South AustraliaSA 5000 AdelaideAustralia Haskayne School of Business University of CalgaryCalgaryAlbertaT2N 1N4Canada

This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a european-type asset by a conic *** price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov *** bid and ask prices of a european-type asset are then characterized using conic quantization.

关键词： Conditional coherent risk measures Markov chains Regime-switching Conic finance european options Distortion functions Conic quantization

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Mean-Variance Hedging for General Claims in an Incomplete Market: Numeraire Method

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Journal of Shanghai Jiaotong university(Science) 2003年第2期8卷 175-178页

作者：王桂兰叶中行 Dept. of Mathematics Shanghai Jiaotong Univ. Shanghai 200030 China

This paper considered the problem of hedging a european call (put) option for a diffusion model where the asset price is influenced by n uncertain factors. The market is thus incomplete implying that perfect hedging is not possible. To derive a hedging strategy, it follows the approach based on the idea of hedging under a mean-variance criterion suggested by Schweizer. A very simple solution of this hedging problem by using the numeraire method was presented and some examples with explicit solutions were given.

关键词： Mean-variance hedging incomplete market numeraire european options

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