VALUATION OF EUROPEAN INSTALLMENT PUT OPTION: VARIATIONAL INEQUALITY APPROACH

2009 ◽  
Vol 11 (02) ◽  
pp. 279-307 ◽  
Author(s):  
ZHOU YANG ◽  
FAHUAI YI
Keyword(s):  
Variational Inequality ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Parabolic Variational Inequality ◽  
Numerical Result ◽  
Put Option ◽  
Uniqueness Of The Solution

In this paper, we consider a parabolic variational inequality arising from the valuation of European installment put option. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain C∞ regularity and the bounds of the free boundary. Eventually, we show its numerical result by the binomial method.

Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

Variational model of sandpile growth

1996 ◽  
Vol 7 (3) ◽  
pp. 225-235 ◽  
Author(s):  
Leonid Prigozhin
Keyword(s):  
Variational Inequality ◽  
Existence And Uniqueness ◽  
Variational Model ◽  
Support Surface ◽  
Uniqueness Of The Solution ◽  
Quasi Variational Inequality ◽  
Steep Slopes

A model describing the evolving shape of a growing pile is considered, and is shown to be equivalent to an evolutionary quasi-variational inequality. If the support surface has no steep slopes, the inequality becomes a variational one. For this case existence and uniqueness of the solution are proved.

scholarly journals Solving Adaptive Image Restoration Problems via a Modified Projection Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Yang ◽  
Xueping Luo ◽  
Leiting Chen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Image Restoration ◽  
Image Denoising ◽  
Existence And Uniqueness ◽  
Experimental Results ◽  
Projection Algorithm ◽  
Tv Regularization ◽  
Uniqueness Of The Solution ◽  
Quasi Variational Inequality

We introduce a new general TV regularizer, namely, generalized TV regularization, to study image denoising and nonblind image deblurring problems. In order to discuss the generalized TV image restoration with solution-driven adaptivity, we consider the existence and uniqueness of the solution for mixed quasi-variational inequality. Moreover, the convergence of a modified projection algorithm for solving mixed quasi-variational inequalities is also shown. The corresponding experimental results support our theoretical findings.

A variational inequality arising from optimal exercise perpetual executive stock options

2017 ◽  
Vol 29 (1) ◽  
pp. 55-77 ◽  
Author(s):  
XIN LAI ◽  
XINFU CHEN ◽  
CONG QIN ◽  
WANGHUI YU
Keyword(s):  
Growth Rate ◽  
Variational Inequality ◽  
Free Boundary ◽  
Discount Rate ◽  
Stock Options ◽  
Return Rate ◽  
Executive Stock Options ◽  
Free Boundaries ◽  
Parabolic Variational Inequality ◽  
Continuous Exercise

We investigate a degenerate parabolic variational inequality arising from optimal continuous exercise perpetual executive stock options. It is also shown in Qinet al.(Continuous-Exercise Model for American Call Options with Hedging Constraints, working paper, available at SSRN:http://dx.doi.org/10.2139/ssrn.2757541) that to make this problem non-trivial the stock's growth rate must be no smaller than the discount rate. Well-posedness of the problem is established in Laiet al.(2015, Mathematical analysis of a variational inequality modeling perpetual executive stock options, Euro. J. Appl. Math., 26 (2015), 193–213), Qinet al.(2015, Regularity free boundary arising from optimal continuous exercise perpetual executive stock options, Interfaces and Free Boundaries, 17 (2015), 69–92), Song & Yu (2011, A parabolic variational inequality related to the perpetual American executive stock options, Nonlinear Analysis, 74 (2011), 6583-6600) for the case when the underlying stock's expected return rate is smaller than the discount rate. In this paper, we consider the remaining case: the discount rate is bigger than the growth rate but no bigger than the return rate. The existence of a unique classical solution as well as a continuous and strictly decreasing free boundary is proved.

Mathematical analysis of a variational inequality modelling perpetual executive stock options

2015 ◽  
Vol 26 (2) ◽  
pp. 193-213 ◽  
Author(s):  
XIN LAI ◽  
XINFU CHEN ◽  
MINGXIN WANG ◽  
CONG QIN ◽  
WANGHUI YU
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Free Boundary ◽  
Control Strategy ◽  
Existence And Uniqueness ◽  
Stock Options ◽  
Executive Stock Options ◽  
Optimal Control Strategy ◽  
Degenerate Parabolic ◽  
Basic Graph

In this paper, we establish the existence and uniqueness of a classical solution of a degenerate parabolic variational inequality of which a strong solution was shown to exist by Song and Yu [21]. The problem arises from optimal stochastic control of exercising continuously perpetual executive stock options (ESOs). We also characterize the basic graph, continuity, and monotonicity properties of the free boundary from which the optimal control strategy can be described precisely.

scholarly journals Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model

2019 ◽  
Vol 12 (2) ◽  
pp. 448-468
Author(s):  
Didier Alain Njamen Njomen ◽  
Eric Djeutcha ◽  
Louis-Aime Fono
Keyword(s):  
Existence And Uniqueness ◽  
Option Price ◽  
Heston Model ◽  
Monte Carlo Algorithm ◽  
Hurst Parameter ◽  
Numerical Result ◽  
Put Option ◽  
Mixed Fractional Brownian Motion ◽  
Heston's Model ◽  
American Put

This paper focuses on a mixed fractional version of Heston model in which the volatility Brownian and price Brownian are replaced by mixed fractional Brownian motion with the Hurst parameter $H\in(\frac{3}{4},1)$ so that the model exhibits the long range dependence. The existence and uniqueness of solution of mixed fractional Heston model is established under various non-Lipschitz condition and a related Euler discretization method is discussed. An example on the American put option price using Least Squares Monte Carlo Algorithm to produce acceptable results under the mixed fractional Heston model is presented to illustrate the applicability of the theory. The numerical result obtained proves the performanceof our results.

scholarly journals A non-local free boundary problem arising in a theory of financial bubbles

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130404 ◽  
Author(s):  
Henri Berestycki ◽  
Regis Monneau ◽  
José A. Scheinkman
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness ◽  
Obstacle Problem ◽  
Speculative Bubbles ◽  
Financial Bubbles ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
The Cost

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c , the cost of transacting the asset, goes to zero.

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