A spectral method for an Optimal Investment problem with transaction costs under Potential Utility

Frutos, Javier de; Gatón, Víctor

doi:10.1016/j.cam.2017.01.015

Cited by 4 publications

(13 citation statements)

References 19 publications

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“…The indifferent price p w (X, t, S) given by ( 8) can be explicitly computed with (11) and is given by…”

Section: The Modelmentioning

confidence: 99%

“…where note that it is independent of the initial wealth p w (X, t, S) = p w (t, S). Substituting (11) into the partial differential equation ( 9), we obtain:…”

Section: The Modelmentioning

confidence: 99%

“…As it is well known, spectral methods (see [5]), are a class of spatial discretizations for partial differential equations with an order of convergence that depends only on the regularity of the function to be approximated. Several papers (see, for example, [3], [9] or [11]) have used spectral methods for problems in Finance with good results. For instance, in [7] a Fourier-Hermite procedure to the valuation of american options is presented.…”

Section: Introductionmentioning

confidence: 99%

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A pseudospectral method for Option Pricing with Transaction Costs under Exponential Utility

de Frutos,

Gaton

2021

Preprint

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This paper concerns the design of a Fourier based pseudospectral numerical method for the model of European Option Pricing with transaction costs under Exponential Utility derived by Davis, Panas and Zariphopoulou in [8]. Computing the option price involves solving two stochastic optimal control problems. With a Exponential Utility function, the dimension of the problem can be reduced, but one has to deal with high absolute values in the objective function. In this paper, we propose two changes of variables that reduce the impact of the exponential growth. We propose a Fourier pseudospectral method to solve the resulting non linear equation. Numerical analysis of the stability, consistency, convergence and localization error of the method are included. Numerical experiments support the theoretical results. The effect of incorporating transaction costs is also studied.

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“…The indifferent price p w (X, t, S) given by ( 8) can be explicitly computed with (11) and is given by…”

Section: The Modelmentioning

confidence: 99%

“…where note that it is independent of the initial wealth p w (X, t, S) = p w (t, S). Substituting (11) into the partial differential equation ( 9), we obtain:…”

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A pseudospectral method for Option Pricing with Transaction Costs under Exponential Utility

de Frutos,

Gaton

2021

Preprint

Self Cite

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“…This issue shows that A is unique. In fact, this set is unique or if the other sets exist, there is just one set to minimize (4). It is the feature of a spectral way.…”

Section: Spectral Linear Filtermentioning

confidence: 99%

“…For example, in the work of Kafash et al, the Chebyshev polynomials are used to solve the optimal control problems. The numerical solution of the finite‐horizon optimal investment problem is discussed in the work of Frutos and Gaton . A direct solution of an optimal control problem is introduced in the work of Mirinejad and Inanc .…”

Section: Introductionmentioning

confidence: 99%

The spectral linear filter method for a stochastic optimal control problem of partially observable systems

Poursherafatan

Delavarkhalafi

2019

Optim Control Appl Methods

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Summary In this paper, two spectral methods are presented to solve a stochastic optimal control problem of a partially observable system. These two methods work together to solve such problems. In fact, solving such problems involves two cases: obtaining the control function and simulating the partially observable system. At first, a spectral linear filter is defined as a function of time to obtain an appropriate solution for a partially observable system. This linear filter is equipped with an orthogonal basis and it is made to predict the future behavior of this system. In this method, the goal is to approximate the trend of the partially observable system. The second method is suggested to achieve the optimal control corresponding to each sample path. In this method, the spectral Fourier transform is used. These two methods are used together to solve linear and nonlinear cases. In fact, the innovative contents of this paper are both the spectral linear filter and the suggested spectral optimal control method.

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Chebyshev reduced basis function applied to option valuation

Frutos

Gatón

2017

Comput Manag Sci

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We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by means of a hierarchical orthogonalization process that allows to reduce the number of degrees of freedom needed to have an accurate representation of the value function. In the paper we consider, as an example, a GARCH model that depends on eight parameters and show that a very large number of contracts for different maturities and asset and parameters values can be valued in a small computational time with the proposed procedure. In particular the method is applied to the problem of model calibration. The method is easily generalizable to be used with other models or problems.

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A spectral method for an Optimal Investment problem with transaction costs under Potential Utility

Cited by 4 publications

References 19 publications

A pseudospectral method for Option Pricing with Transaction Costs under Exponential Utility

A pseudospectral method for Option Pricing with Transaction Costs under Exponential Utility

The spectral linear filter method for a stochastic optimal control problem of partially observable systems

Chebyshev reduced basis function applied to option valuation

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