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In this paper, the valuation of European options in which the underlying stock pays a discrete dividend is investigated. A specific value is set in advance, and a dividend is paid when the underlying share price reaches it. The risk-neutral price of the associated European call option is derived. Numerical simulations are presented to illustrate the effects of model parameters on the option prices. [ABSTRACT FROM AUTHOR]

In this paper, stochastic Gilpin-Ayala model driven by α-stable process under regime switching is presented. Firstly, we prove the existence and uniqueness of the solution for the stochastic model. Then, under certain conditions, the almost sure exponential stability and pth moment exponential stability of the trivial solution are obtained. The results indicated that the α-stable noises can make the trivial solution stable under some conditions. Computer simulations are presented to illustrate our theory. [ABSTRACT FROM AUTHOR]

This article considers the optimal reinsurance-portfolio problem that the insurer invests in two related risky assets described by different types: constant elasticity of variance model and jump-diffusion process model, besides a risk-free asset. There is a correlation between the diffusion processes of the two models. Meanwhile, the company purchases proportional reinsurance. Specially, assume the claim process follows a Lévy process and the reinsurance's premium principle has not to be certain. Then based on stochastic control theory, a novel form of the optimal value function for solving the Hamilton-Jacobi-Bellman equation is constructed. Finally, the expressions of the optimal results are obtained under maximizing the expected exponential utility of terminal wealth. In addition, we listed several examples of the common premium principles. Numerical simulations are supplied for sensitivity analysis of parameters. [ABSTRACT FROM AUTHOR]

This paper is concerned with the parameter estimation problem for generalized Ait-Sahalia-type interest rate model based on discrete observation. The parameter estimators are obtained by applying the approximate maximum likelihood estimation, ergodic theorem and properties of quadratic variation. The strong consistency property of parameter estimators is proved by using the law of large numbers for martingales and properties of quadratic covariation. Computer simulations are performed to illustrate our theory. [ABSTRACT FROM AUTHOR]

In this paper, the valuation of European option is investigated when the discrete dividends are described by Markov-modulated Merton jump-diffusion process. According to the dividend discount theory, we regard the stock price as the net present value of all future dividends. The regime switching Esscher transform is applied to determine a risk-neutral measure. The closed form solution of European option is obtained under the condition that the dividend payments are announced in advance. Numerical simulations for the European call option prices are provided. [ABSTRACT FROM AUTHOR]

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset. Especially the price process of the risky asset is governed by Heston's stochastic volatility ( SV) model. With the objective of maximizing the expected index utility of the terminal wealth of the insurance company, by using the classical tools of stochastic optimal control, the explicit expressions for optimal strategies and optimal value functions are derived. An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper. Moreover, some numerical simulations and sensitivity analysis are provided. [ABSTRACT FROM AUTHOR]

This paper is concerned with the filtering problem for a class of discrete-time stochastic nonlinear networked control systems with network-induced incomplete measurements. The incomplete measurements include both the multiple random communication delays and random packet losses, which are modeled by a unified stochastic expression in terms of a set of indicator functions that is dependent on certain stochastic variable. The nonlinear functions are assumed to satisfy the sector nonlinearities. The purpose of the addressed filtering problem is to design a linear filter such that the filtering-error dynamics is exponentially mean-square stable. By using the linear-matrix-inequality (LMI) method and delay-dependent technique, sufficient conditions are derived which are dependent on the occurrence probability of both the random communication delays and missing measurement. The filter gain is then characterized by the solution to a set of LMIs. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures. Index Terms--Exponential mean-square stability, networked control system (NCS), random communication delay, random packet loss, sector nonlinearity, stochastic disturbance.