A note on the theory of the firm under multiple uncertainties

Alghalith, Moawia

doi:10.1016/j.ejor.2015.12.003

Cited by 9 publications

(5 citation statements)

References 13 publications

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“…We use a stochastic portfolio model (see, for example, [1,2,4,6,7]) with a standard Brownian motion {W 1s , F s } t≤s≤T defined on the probability space (Ω, F , F s , P), where {F s } t≤s≤T is the augmentation of filtration. The price of a risk-free asset is given by…”

Section: The Modelmentioning

confidence: 99%

A Note on a New Approach to Both Price and Volatility Jumps: An Application to the Portfolio Model

Alghalith

2016

ANZIAM J.

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A new approach to jump diffusion is introduced, where the jump is treated as a vertical shift of the price (or volatility) function. This method is simpler than the previous methods and it is applied to the portfolio model with a stochastic volatility. Moreover, closed-form solutions for the optimal portfolio are obtained. The optimal closed-form solutions are derived when the value function is not smooth, without relying on the method of viscosity solutions.

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Section: The Modelmentioning

confidence: 99%

A Note on a New Approach to Both Price and Volatility Jumps: An Application to the Portfolio Model

Alghalith

2016

ANZIAM J.

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“…Meanwhile, we assume that the similar product has been traded in the market. Following the idea of [12], we assume that the price of the similar product is exogenously determined, which follows a geometric Brownian motion process:…”

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“…However, the problem ( 5) is a classic problem so that we omit the verification theorem here. Moreover, the free boundary problem (12) cannot obtain any closed-form solution so we give some numerical examples in section 4 . Now, we solve the optimal release problem (6).…”

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“…where F (x) and X * can be obtained by (12). Substituting ( 12) and ( 15) into ( 14), respectively, ( 14) can be reduced to the following VI…”

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“…In Table 1, the value for the investment cost of the R&D project parameters such as β, I * , V are set in the spirit of the investment of R&D project with technical uncertainty literature (see, e.g, [11], [13] and [17]). The parameters relating to the price of the similar product such as σ, α and r are set similarly to [6] and [12]. Moreover, we set the market value parameters δ 1 and δ 2 according to the example in [7].…”

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Optimal product release time for a new high-tech startup firm under technical uncertainty

Wang

Huang

O’Regan

2023

JIMO

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<p style='text-indent:20px;'>Decision makers of new high-tech startup firms always want to choose an optimal time to launch their products which are under research and development (R&D) to obtain the maximum net income of these firms. However, existing models fail to consider the optimal release time of products for these new high-tech startup firms. In this paper, the optimal time to launch the product of the R&D project is assumed to be the first time when the product of the R&D project is released to the market. Based on this assumption, we develop a continuous-time model to find the optimal time at which the startup firm launches its product of the R&D project by considering the price of the similar product. Employing the methods of dynamic programming and variational inequalities, we also provide a closed form solution to our model. We also find that these high-tech startup firms prefer to delay their product release time when the price of the similar product is at a phase of rapid growth or the price has considerable uncertainty. Moreover, some numerical examples are provided to investigate the properties of our model.</p>

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