Valuation of stock loan under uncertain mean-reverting stock model

Shi, Gang; Zhang, Zhiqiang; Sheng, Yuhong

doi:10.3233/jifs-17378

Cited by 9 publications

(3 citation statements)

References 36 publications

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“…Later, Yao ( 2015b ) proved the no-arbitrage theorem of this uncertain stock model, Chen ( 2011 ) derived the American option price formula, and Sun and Chen ( 2015 ) developed the Asian option price formula. Besides these, other scholars have pioneered or improved those families of uncertain models with mean regression (Yao, 2012 ; Sun & Su, 2017 ; Shi et al, 2017 ; Sun et al, 2018a ; Tian et al, 2019 ; Yao & Qin, 2021 ), periodic dividends or jumps (Yu, 2012 ; Chen et al, 2013 ; Ji & Zhou, 2014 ), and uncertain currency models with floating interest rates (Liu et al, 2015a ; Wang & Ning, 2017b ; Ji & Wu, 2017 ; Wang & Chen, 2019 ) to derive European, American and Asian option pricing formulas. The uncertain interest rate model is generally used for the valuation of zero-coupon bonds (Jiao & Yao, 2015 ; Sun et al, 2018b ) and the calculation of some upper and lower limits (Zhang et al, 2016 ; Mehrdoust & Najafi, 2019 ).…”

Section: Discussion Of Development Historymentioning

confidence: 99%

A systematic review of uncertainty theory with the use of scientometrical method

Zhou

Jiang

Pantelous

et al. 2022

Fuzzy Optim Decis Making

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Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.

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Section: Discussion Of Development Historymentioning

confidence: 99%

A systematic review of uncertainty theory with the use of scientometrical method

Zhou

Jiang

Pantelous

et al. 2022

Fuzzy Optim Decis Making

View full text Add to dashboard Cite

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“…the bank) to whom the stock is transferred after providing to the borrower a loan [9,10]. The lender can become the owner of the stock in case that the borrower fails to pay back his loan [11][12][13][14][15][16][17][18]. In such a loan agreement, the borrower may retrieve the stock an any time before or on the maturity, where maturity is the agreed time for paying back the loan [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…In such a loan agreement, the borrower may retrieve the stock an any time before or on the maturity, where maturity is the agreed time for paying back the loan [13,14]. The value of the stock loan is the difference between the cumulative value of the stock minus the accumulated interest according to the agreed interest rate [15,16]. The valuation problem of stock loans is a non-trivial one because the model of a stock-loan's price is complicated and is described either in the form of a stochastic differential equation or in the form of a partial differential equation [17,[19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of a stock‐loan valuation PDE process using differential flatness theory

Rigatos

Siano

Loia

et al. 2019

Asian Journal of Control

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The article proposes flatness-based control for stabilization of a stock-loan valuation process that is described by a partial differential equation. By applying semi-discretization and the finite differences method, the state-space model of the stock loan has been obtained. It has been proven that the individual rows of this state-space model are nonlinear ODEs which can be viewed as differentially flat subsystems. For the local subsystems, into which the stock-loan PDE is decomposed, it becomes possible to apply boundary feedback control. The controller design proceeds by showing that the state-space model of the stock loan PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the stock loan PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space description. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the stock loan PDE system so as to assure that all its state variables will converge to the desirable setpoints.By showing the feasibility of such a control method it is also proven that through selected modification of the PDE boundary conditions the value of the stock loan can be made to converge and stabilize at specific reference values.

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Power Option Pricing Problem Based on Uncertain Mean-Reverting Stock Model with Floating Interest Rate

Huang

Yang

2019

Proceedings of the Sixth International Forum on Decision Sciences

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Valuation of stock loan under uncertain mean-reverting stock model

Cited by 9 publications

References 36 publications

A systematic review of uncertainty theory with the use of scientometrical method

A systematic review of uncertainty theory with the use of scientometrical method

Stabilization of a stock‐loan valuation PDE process using differential flatness theory

Power Option Pricing Problem Based on Uncertain Mean-Reverting Stock Model with Floating Interest Rate

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