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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]

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]

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]

In this paper, we investigate optimal frame-selection algorithms based on dynamic programming for delivering stored variable bit rate (VBR) video under both bandwidth and buffer size constraints. Our objective is to find a feasible set of frames that can maximize the video's accumulated motion values without violating any constraint. It is well known that dynamic programming has high complexity. In this research, we propose to eliminate nonoptimal intermediate frame states, which can effectively reduce the complexity of dynamic programming. Moreover, we propose a reverse frame selection (RFS) algorithm, where the selection starts from the last frame and ends at the first frame. Compared with the conventional dynamic programming-based forward frame selection, the RFS is able to find all of the optimal results for different preloads in one round. We further extend the RFS scheme to solve the problem of frame selection for VBR channels. In particular, we first perform the RFS algorithm offline, and the complexity is modest and scalable with the aids of frame stuffing and nonoptimal state elimination. During online streaming, we only need to retrieve the optimal frame-selection path from the pregenerated offline results, and it can be applied to any VBR channels as long as the VBR channels can be modeled as piecewise CBR channels. Experimental results show good performance of our proposed algorithms. Index Terms--Bandwidth smoothing, dynamic programming, motion awareness, optimal frame selection, variable bit rate (VBR) channels, VBR video delivery.

The present article deals with the problem of parametric estimation for certain nonstationary processes driven by α-stable motions. The trajectory fitting method combined with the weighted least squares technique is used to obtain an estimator of the drift parameter. The asymptotic behavior of the weighted trajectory fitting estimator for general weights in non-ergodic case, including consistency and asymptotic distribution. [ABSTRACT FROM AUTHOR]

This present paper deals with the problem of stabilization and destabilization of nonlinear stochastic differential delay equations. The key techniques used in this paper are the LaSalle-type stability theorems, the nonnegative semimartingale convergence theorem, and the law of large numbers for martingales. The proposed results can be applied to study the stabilization and destabilization of more general nonlinear stochastic dynamical time-delay systems. Computer simulations are presented to illustrate our theory. [ABSTRACT FROM AUTHOR]