Algorithm for Determining the Volatility Function in the Black–Scholes Model

Isakov, Victor; Кабанихин, С. И.; Шананин, А. А.; Shishlenin, Maxim A.; Zhang, S.

doi:10.1134/s0965542519100099

Cited by 13 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Despite the small amount of known data, we managed to make an assumption regarding the time of the mutations' accumulation to a number sufficient for the appearance of visible differences in individuals in the mouse population and found that the initial set of mice in the experiment described in [22] already consisted of at least two phenotypically different groups of mice. This result was possible thanks to the active development of methods for solving coefficient inverse problems for partial differential equations with data on curves inside the domain (see [34][35][36][37][38][39]).…”

Section: Discussionmentioning

confidence: 99%

Modeling the Dynamics of Negative Mutations for a Mouse Population and the Inverse Problem of Determining Phenotypic Differences in the First Generation

et al. 2023

View full text Add to dashboard Cite

This paper considers a model for the accumulation of mutations in a population of mice with a weakened function of polymerases responsible for correcting DNA copying errors during cell division. The model uses the results of the experiment published by Japanese scientists, which contain data on the accumulation of phenotypic differences in three isolated groups of laboratory mice. We have developed a model for the accumulation of negative mutations. Since the accumulation of phenotypic differences in each of the three groups of mice occurred in its own way, we assumed that these differences were associated with genotypic differences in the zeroth generation and set the inverse problem of determining the initial distribution of these differences. Additional information for solving the inverse problem was a set of experimental data on the number of mutant lines and the number of individuals in each group of mice. The results obtained confirmed our assumption.

show abstract

Section: Discussionmentioning

confidence: 99%

Modeling the Dynamics of Negative Mutations for a Mouse Population and the Inverse Problem of Determining Phenotypic Differences in the First Generation

et al. 2023

View full text Add to dashboard Cite

show abstract

“…Problems for nonlinear singularly perturbed reaction-diffusion-advection equations arise in gas dynamics [1], combustion theory [2], chemical kinetics [3][4][5][6][7][8][9][10], nonlinear wave theory [11], biophysics [12][13][14][15][16], medicine [17][18][19][20], ecology [21][22][23][24][25], finance [26] and other fields of science [27]. A specific feature of problems of this type is the presence of processes of different scales.…”

Section: Introductionmentioning

confidence: 99%

Inverse Problem for an Equation of the Reaction-Diffusion-Advection Type with Data on the Position of a Reaction Front: Features of the Solution in the Case of a Nonlinear Integral Equation in a Reduced Statement

et al. 2021

View full text Add to dashboard Cite

The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse problem. An important question arises: is it possible to obtain a mathematical connection between the unknown coefficient and the data of the inverse problem? The methods of asymptotic analysis of the direct problem help to solve this question. But the reduced statement of the inverse problem obtained by the methods of asymptotic analysis contains a nonlinear integral equation for the unknown coefficient. The features of its solution are discussed. Numerical experiments demonstrate the possibility of solving problems of such class using the proposed methods.

show abstract

“…Nonlinear singularly perturbed reaction-diffusion-advection equations arise when solving the problems in gas dynamics [1], combustion theory [2], chemical kinetics [3][4][5][6][7][8][9], nonlinear wave theory [10], biophysics [11][12][13][14][15], medicine [16][17][18][19], ecology [20][21][22], finance [23], and other areas of science [24]. Inverse problems for the equation of this type often arise when solving various applied problems and consist of recovering some coefficient in the equation.…”

Section: Introductionmentioning

confidence: 99%

On Some Features of the Numerical Solving of Coefficient Inverse Problems for an Equation of the Reaction-Diffusion-Advection-Type with Data on the Position of a Reaction Front

et al. 2021

View full text Add to dashboard Cite

The work continues a series of articles devoted to the peculiarities of solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection-type with data on the position of the reaction front. In this paper, we place the emphasis on some problems of the numerical solving process. One of the approaches to solving inverse problems of the class under consideration is the use of methods of asymptotic analysis. These methods, under certain conditions, make it possible to construct the so-called reduced formulation of the inverse problem. Usually, a differential equation in this formulation has a lower dimension/order with respect to the differential equation, which is included in the full statement of the inverse problem. In this paper, we consider an example that leads to a reduced formulation of the problem, the solving of which is no less a time-consuming procedure in comparison with the numerical solving of the problem in the full statement. In particular, to obtain an approximate numerical solution, one has to use the methods of the numerical diagnostics of the solution’s blow-up. Thus, it is demonstrated that the possibility of constructing a reduced formulation of the inverse problem does not guarantee its more efficient solving. Moreover, the possibility of constructing a reduced formulation of the problem does not guarantee the existence of an approximate solution that is qualitatively comparable to the true one. In previous works of the authors, it was shown that an acceptable approximate solution can be obtained only for sufficiently small values of the singular parameter included in the full statement of the problem. However, the question of how to proceed if the singular parameter is not small enough remains open. The work also gives an answer to this question.

show abstract

Algorithm for Determining the Volatility Function in the Black–Scholes Model

Cited by 13 publications

References 16 publications

Modeling the Dynamics of Negative Mutations for a Mouse Population and the Inverse Problem of Determining Phenotypic Differences in the First Generation

Modeling the Dynamics of Negative Mutations for a Mouse Population and the Inverse Problem of Determining Phenotypic Differences in the First Generation

Inverse Problem for an Equation of the Reaction-Diffusion-Advection Type with Data on the Position of a Reaction Front: Features of the Solution in the Case of a Nonlinear Integral Equation in a Reduced Statement

On Some Features of the Numerical Solving of Coefficient Inverse Problems for an Equation of the Reaction-Diffusion-Advection-Type with Data on the Position of a Reaction Front

Contact Info

Product

Resources

About