Journal of Mathematical Finance

Journal Information
ISSN / EISSN : 21622434 / 21622442
Current Publisher: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 397
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Latest articles in this journal

Liangliang Zhang, Zhang Liangliang
Journal of Mathematical Finance, Volume 10, pp 1-9; doi:10.4236/jmf.2020.101001

Abstract:In this paper, we introduce a clustering method to approximate the solution to a general Backward Stochastic Differential Equation with Jumps (BSDEJ). We show the convergence of the sequence of approximate solutions to the true one. The method is implemented for an application in finance. Numerical results show that the method is efficient.
Lusungu Julius Mbigili, Sure Mataramvura, Wilson M. Charles
Journal of Mathematical Finance, Volume 10, pp 10-26; doi:10.4236/jmf.2020.101002

Abstract:This work presented and solved the problem of portfolio optimization within the context of continuous-time stochastic model of financial variables. It has considered an investment problem of two assets, namely, risk-free assets and risky assets. The evolution of the risk-free asset is described deterministically while the dynamics of the risky asset is described by the geometric mean reversion (GMR) model. The controlled wealth stochastic differential Equation (SDE) and the optimal portfolio problem were successfully formulated and solved with the help of the theory of stochastic control technique where the dynamic programming principle (DPP) and the HJB theory were used. Two utility functions which are members of hyperbolic absolute risk aversion (HARA) family have been employed, and these are power utility and exponential utility. In both cases, the optimal control has explicit form and is wealth dependent Linearization of the logarithmic term in the portfolio problem was necessary for simplification of the problem.
Chuankang Chai
Journal of Mathematical Finance, Volume 10, pp 27-34; doi:10.4236/jmf.2020.101003

Abstract:We use the G-geometric Brownian motion and G-quadratic variation process to describe the price change of the asset. We prove that American call options do not pay dividends under G-framework. Finally we can simulate the stock price under the numerical simulation of G-brown motion and G-quadratic variation process.
Liyang Feng
Journal of Mathematical Finance, Volume 10, pp 35-41; doi:10.4236/jmf.2020.101004

Abstract:In the G-expectation framework, Wang [1] first obtained the Jensen inequality of one-dimensional function. In this paper, under some stronger conditions, we obtain the Jensen inequality of bivariate function based on Wang’s proof method. And we give some examples to illustrate the application of Jensen inequality of bivariate function.
Jane Mpapalika
Journal of Mathematical Finance, Volume 10, pp 42-57; doi:10.4236/jmf.2020.101005

Abstract:This paper investigates the alternative financing instruments that can be used to hedge sovereign risks and finance development in African countries. Many heavily indebted countries are exposed to external risks especially the exchange rate shocks due to limited use of hedging instruments. We propose alternative financing instruments to minimize sovereign risks and the cost of debt. Our paper uses the standard model for pricing options, the Black-Scholes model to determine the fair value of options. The findings show that barrier options have an added advantage over plain vanilla options because of its knock-ins and knock-outs features hence they are the most affordable to use. An important aspect of the effective debt management policies should be on developing local bond market to access alternative financing instruments in the world capital market.
Jiang Xiangxi, Xiangxi Jiang
Journal of Mathematical Finance, Volume 10, pp 132-139; doi:10.4236/jmf.2020.101009

Abstract:Bitcoin is a current popular cryptocurrency with a promising future. It’s like a stock market with time series, the series of indexed data points. We looked at different deep learning networks and methods of improving the accuracy, including min-max normalization, Adam optimizer and windows min-max normalization. We gathered data on the Bitcoin price per minute, and we rearranged them to reflect Bitcoin price in hours, a total of 56,832 points. We took 24 hours of data as input and output the Bitcoin price of the next hour. We compared the different models and found that the lack of memory means that Multi-Layer Perceptron (MLP) is ill-suited for the case of predicting price based on current trend. Long Short-Term Memory (LSTM) provides relatively the best prediction when past memory and Gated Recurrent Network (GRU) is included in the model.
Hongduo Cao, Zerui Guo, Ying Li, Zhouzhou Ran
Journal of Mathematical Finance, Volume 10, pp 58-76; doi:10.4236/jmf.2020.101006

Abstract:The optimal threshold strategy is put forward for establishing a suitable network for analyzing the correlation among the different exchange rates. The 33 currencies of the world’s major countries and regions are analyzed by the method of network analysis, and the multilateral exchange rate correlation network is established based on the optimal threshold. Combining with geographical features and the exchange rate regime, it is found that the international currency has obvious community structure, which is composed of three levels: the core currency area, the arbitrage currency area and the shadow currency area. The conclusion reveals the structural characteristics of the Jamaica international monetary system.
Zhenzhong Guan, Hezhi Chen, Na Zhao, Aifeng Zhang
Journal of Mathematical Finance, Volume 10, pp 96-131; doi:10.4236/jmf.2020.101008

Abstract:Combined with the development of Chinese medical industry, we have analyzed the characteristics of the referral system with Chinese characteristics and the possible problems in it. We combine the two main factors that affect patient care: medical quality and waiting costs, to study a most representative referral system made up of a tertiary hospital and a community hospital for its pricing and capacity planning issues. We build an integrated model of queuing theory and game theory to analyze if all patients make rational choices, what the community hospital should do to maximize the service capacity. Meanwhile, how the tertiary hospital makes pricing to achieve its profit maximization in the case of government taxation. The results show that the service capacity of community hospital is affected by government subsidies, cure rate, and the medical expenses of the tertiary hospital. And those of tertiary hospital are influenced most by government subsidies. Therefore, the results show that the smooth implementation of the government’s macro-control plays a crucial role in the two-way referral system.
Xinlan Ye, Zhenzhong Guan, Miao Ouyang
Journal of Mathematical Finance, Volume 10, pp 77-95; doi:10.4236/jmf.2020.101007

Abstract:This article mainly considers the impact of cost reduction on price matching strategy when a firm sells products in two periods. The cost reduction in the second period is due to technological advancement and production learning. The market is made up of myopic consumers and strategic consumers. The conclusions show that firm’s optimal profit will decrease with the increase of the fraction of strategic consumers. Besides, when the production learning effect dominates, the firm sells at a reduced price in two periods. When the technological advancement effect dominates, the firm maintains a uniform price for sale throughout the sales period. Finally, both the technological advancement and production learning effect can effectively reduce the loss of profits caused by strategic consumers, and the effect of the technological advancement is more significant.
M. Pucci
Journal of Mathematical Finance, Volume 9, pp 301-324; doi:10.4236/jmf.2019.93018