Author(s)

TengLong Wang^1*, Chen Ai²

Affiliation(s)

¹ Department of Finance, Shanghai University, Shanghai 200444, China.

² Department of Mathematics, Columbia University, New York 10027, U.S.

Corresponding Author

TengLong Wang

ABSTRACT

This paper aims to solve the problem of how investors make the best decisions when facing incomplete information and risk situations in the real financial market. This paper uses the polynomial tree, diffusion process, and Vasicek models to study the optimal stopping time problem under fuzzy asset information. Specifically, the trinomial tree model of asset prices is constructed first. The model simulates the movement of asset prices in different states by setting three branches at each node (price rise, price fall, and price unchanged). The key to constructing a trinomial tree is to set each node's transfer probability and price range reasonably. Second, this paper analyses the changes in the multi-prior distribution of asset prices under different parameter settings. The theory of diffusion process is applied to the problem of optimal stopping time. Moreover, the Vasicek model is employed to describe the random fluctuation of interest rate, and determining the optimal stopping time under various diffusion processes is studied by deducing the Laplace transform expression that reaches a specific level for the first time. The key of the Vasicek model is that it reflects the average regression characteristic of interest rates. Here, the Laplace transform function image corresponding to the first occurrence time under the conditions of these parameters is drawn by using a numerical calculation method and selecting different parameter values. Lastly, the optimal stopping time problem of American put options in the diffusion risk model with drift coefficient is studied. By constructing a mathematical model of the stochastic process and its stopping time, the optimal value function and optimal transaction time are derived. Numerical example analysis shows that when the parameter λ is 0, the value of the Laplace transform for the first exit T_b of T_b<T_a decreases overall. In the case of fixed drift parameter с and random volatility σ, as the value of interest rate r increases, the corresponding value of the optimal stopping time also increases. Under the condition of fuzzy asset information, this paper provides a reference for providing more accurate decision support for decision-makers and researchers in the financial field.

KEYWORDS

Fuzzy asset information; Optimal stopping algorithm; Trinomial tree; Diffusion process; Vasicek model

CITE THIS PAPER

Tenglong Wang, Chen Ai. Optimal stopping algorithm and its application under the condition of fuzzy asset information. World Journal of Management Science. 2024, 2(1): 42-52. DOI: 10.61784/wmsv2n185.

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