Exact Simulation of the First-Passage Time of Diffusions

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson in J Financ Quant Anal 18(1):141–148 (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same efficiency as the quadratic approximation of Barone-Adesi and Whaley in J Financ 42:301–320 (1987), with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston’s stochastic volatility model, our method is shown to be extremely efficient and fairly accurate.

General References, Diffusion Processes, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

A Closed-Form Solution to American Options under General Diffusions

A novel multi-term time-fractional mixed diffusion and diffusion-wave equation will be considered in this work. Different from the general multi-term time-fractional mixed diffusion and diffusion-wave equations, this new multi-term equation possesses a special time-fractional operator on the spatial derivative. We use a new discrete scheme to approximate the time-fractional derivative, which can improve the temporal accuracy. Then, a fully discrete spectral scheme is developed based on finite difference discretization in time and Legendre spectral approximation in space. Meanwhile, a very important lemma is proposed and proved, to obtain the unconditional stability and convergence of the fully discrete spectral scheme. Finally, four numerical experiments are presented to confirm our theoretical analysis. Both of our analysis and numerical test indicate that the fully discrete scheme is accurate and efficient in solving the generalized multi-term time-fractional mixed diffusion and diffusion-wave equation.

We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times.

Time and value throughputs reflect the actual workload and gross profit of enterprises over a period of time, respectively. Both of them are of great importance to the operation of data-aware workflow processes, since they can help managers to balance production capacity at each stage as well as determine how much capital should be recycled over a period of time. However, the existing methods have not investigated both time and value throughputs of data-aware workflow processes. In this paper, we propose a new approach to modeling and simulation of time and value throughputs of data-aware workflow processes. First of all, we construct an abstract model with time and value elements. Second, the abstract model is transformed into a simulation model in CPN Tools. Finally, we obtain and analyze the time and value throughputs automatically via the simulation logs. Compared with the existing methods, this is the first attempt to propose both time and value throughputs of data-aware workflow processes, and the whole procedure of modeling and simulation of them. Furthermore, the procedure of obtaining time and value throughputs through analyzing the logs is proposed, and a prototype system is designed and developed.

Generalizing the hypergraph Laplacian via a diffusion process with mediators

Many fluctuation phenomena, in physics and other fields, can be modeled byFokker–Planck or stochastic differential equations whose coefficients, associated with driftand diffusion components, may be estimated directly from the observed time series. Itscorrect characterization is crucial to determine the system quantifiers. However, due to thefinite sampling rates of real data, the empirical estimates may significantly differ from theirtrue functional forms. In the literature, low-order corrections, or even no corrections, havebeen applied to the finite-time estimates. A frequent outcome consists of lineardrift and quadratic diffusion coefficients. For this case, exact corrections havebeen recently found, from Itô–Taylor expansions. Nevertheless, model validationconstitutes a necessary step before determining and applying the appropriatecorrections. Here, we exploit the consequences of the exact theoretical results obtainedfor the linear–quadratic model. In particular, we discuss whether the observedfinite-time estimates are actually a manifestation of that model. The relevanceof this analysis is put into evidence by its application to two contrasting realdata examples in which finite-time linear drift and quadratic diffusion coefficientsare observed. In one case the linear–quadratic model is readily rejected while inthe other, although the model constitutes a very good approximation, low-ordercorrections are inappropriate. These examples give warning signs about the properinterpretation of finite-time analysis even in more general diffusion processes.

Bayesian testing for short term interest rate models

An increased cooperation between universities and industries is seen by many politicians as an ultimate remedy against economic under-development by fostering regional growth in a world in which the know-how content of products is ever increasing. Furthermore, this know-how is increasingly separable from the goods and, thus, can be developed into an Intellectual Property Right (IPR). As we well know, technological development was historically often linked to the machinery in which this specific technology was used, and enterprises tried to keep implicit knowledge within their firms, protecting it against diffusion into economic space. The more that know-how became public, for instance through the development within publicly financed research units, such as universities, the more a general diffusion process became possible. It was in the nineteenth century that nation-states started to found their universities of technology, their royal research institutes, etc. in order to promote technological development. The necessity to protect generally accessible know-how that was privately developed became of strategic importance and, thus, international regulations on trade marks, patents, their licensing, etc. developed.

A new frequency-domain discretization technique that permits the numerical solution of the equation governing the propagation of small disturbances within nonuniform potential flows is described. The method can be applied successfully to the numerical solution of aeroacoustic problems because a good accuracy is preserved up to 3-4 points per period for three-dimensional unstructured meshes. The discretization scheme is based on a local interpolation formula that is strictly joined to the physics of wave propagation because It is constructed with the superimposition of elementary sources that are local solutions of the local convective wave equation. The method presents aspects in common with both finite difference and finite element methods, with the peculiarity that the local interpolation formula can be interpreted as a specific shape function introduced to take advantage of the physics of the problem. The method is applied to the potential equation linearized around an arbitrary aerodynamic mean flow, and several comparisons with theoretical results, as well as several convergence tests, are conducted to show that a good accuracy is preserved up to 3-4 points per period also for irregular meshes with both random and Systematic distortions. Numerical calculations are presented for three-dimensional problems with both uniform and nonuniform flow, and comparisons are made with theoretical and other available numerical results. With the appropriate generalizations, the method can be regarded as a new, efficient general approach for the discretization of generic partial differential equations.

The forward-path method for pricing multi-asset American-style options under general diffusion processes

A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg–de Vries equation