On an optimal control problem

Yıldız, Bünyamin; Yagubov, Gabil

doi:10.1016/s0377-0427(97)00198-2

Cited by 10 publications

(4 citation statements)

References 5 publications

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“…However, we have not found any counterexample to indicate the non-uniqueness of the solution in the case when T is large. In general, the solution obtained by numerical computations is unique (see [3,15]) though the uniqueness of the solution is not proved theoretically. Hence people may still take T relatively large in practice.…”

Section: Remarkmentioning

confidence: 99%

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An inverse problem of determining the implied volatility in option pricing

Deng

Jiang

Yang

2008

Journal of Mathematical Analysis and Applications

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In the Black-Scholes world there is the important quantity of volatility which cannot be observed directly but has a major impact on the option value. In practice, traders usually work with what is known as implied volatility which is implied by option prices observed in the market. In this paper, we use an optimal control framework to discuss an inverse problem of determining the implied volatility when the average option premium, namely the average value of option premium corresponding with a fixed strike price and all possible maturities from the current time to a chosen future time, is known. The issue is converted into a terminal control problem by Green function method. The existence and uniqueness of the minimum of the control functional are addressed by the optimal control method, and the necessary condition which must be satisfied by the minimum is also given. The results obtained in the paper may be useful for those who engage in risk management or volatility trading.

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Section: Remarkmentioning

confidence: 99%

“…In this paper, we use an optimal control framework [11,16] to discuss Problem P2 from the theoretical analysis angle (see [3,15] which also used the optimal control method, but focused more on numerical computations). The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

An inverse problem of determining the implied volatility in option pricing

Deng

Jiang

Yang

2008

Journal of Mathematical Analysis and Applications

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“…On the basis of adopted assumptions, the results of [6], and the results obtained by using Galerkin method [3][4][5][6], it follows that for every t ∈ V the solution of the problem (2)- (5) exists in the space B 0 and is unique, and for this solution the following estimate is valid:…”

Section: Letmentioning

confidence: 99%

“…Such problems were investigated in [2][3][4]. Optimal control problem for nonstationary Schrödinger equation of quasi-optic was investigated for the first time in [5]. This article is concerned with finding the minimum of the functional…”

Section: Introductionmentioning

confidence: 99%